PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 6.6, Problem 61E

(a)

To determine

To calculate:

The trigonometric form of following complex number:

  (2+2i)(1i)

(a)

Expert Solution
Check Mark

Answer to Problem 61E

The trigonometric from of given complex number is

  4(cosπ4+isinπ4)(cos(π4)+isin(π4)) .

Explanation of Solution

Given information:

  (2+2i)(1i)

Calculation:

Consider,

  z1=(2+2i)z2=(1i)

For z1=(2+2i) :

Compare z1=(2+2i) with z=a+bi :

  a=2b=2

The modulus is calculated as:

  r=a2+b2r=(2)2+(2)2r=4+4r=22

The argument is calculated as:

  θ=tan1(ba)θ=tan1(22)θ=tan1(1)θ=π4

The trigonometric form of the complex number is calculated as:

  z1=r(cosθ+isinθ)z1=22(cosπ4+isinπ4)

For z2=(1i) :

Compare z2=(1i) with z=a+bi :

  a=1b=1

The modulus is calculated as:

  r=a2+b2r=(1)2+(1)2r=2r=2

The argument is calculated as:

  θ=tan1(ba)θ=tan1(11)θ=tan1(1)θ=π4

The trigonometric form of the complex number is calculated as:

  z2=r(cosθ+isinθ)z2=2(cos(π4)+isin(π4))

Therefore, trigonometric form for the given complex number is calculated as:

  (2+2i)(1i)=[22(cosπ4+isinπ4)][2(cos(π4)+isin(π4))](2+2i)(1i)=4(cosπ4+isinπ4)(cos(π4)+isin(π4))

(b)

To determine

To calculate:

The product of complex number of the trigonometric form from subpart (a)

(b)

Expert Solution
Check Mark

Answer to Problem 61E

The product of complex number of the trigonometric form is [22(cosπ4+isinπ4)][2(cos(π4)+isin(π4))]=4[cos(π2)+isin(π2)]

Explanation of Solution

Given information:

  [22(cosπ4+isinπ4)][2(cos(π4)+isin(π4))]

Formula used:

The multiplication rule for two complex numbers:

  z1z2=r1(cosθ1+isinθ1)r2(cosθ2+isinθ2)z1z2=r1r2[cos(θ1+θ2)+isin(θ1+θ2)]

Calculation:

The multiplication of complex number is calculated as:

  [22(cosπ4+isinπ4)][2(cos(π4)+isin(π4))]

On comparing it with formula:

  r1=22,r2=2,θ1=π4,θ2=π4

Now, [22(cosπ4+isinπ4)][2(cos(π4)+isin(π4))]=222[cos(π4+π4)+isin((π4)+(π4))][22(cosπ4+isinπ4)][2(cos(π4)+isin(π4))]=4[cos(π2)+isin(π2)]

(c)

To determine

To calculate:

The product of complex number of the standard form

(c)

Expert Solution
Check Mark

Answer to Problem 61E

The product of complex number of the standard form is 3 .

Explanation of Solution

Given information:

  (2+2i)(1i)

Calculation:

Know that:

The multiplication of given two vectors (2+2i) and (1i) is calculated as:

  (2+2i)(1i)=22i+2i2i2(2+2i)(1i)=2+2(2+2i)(1i)=4

Chapter 6 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - 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Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Prob. 40ECh. 6.3 - Prob. 41ECh. 6.3 - Prob. 42ECh. 6.3 - Prob. 43ECh. 6.3 - Prob. 44ECh. 6.3 - Prob. 45ECh. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - Prob. 49ECh. 6.3 - Prob. 50ECh. 6.3 - Prob. 51ECh. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Prob. 55ECh. 6.3 - Prob. 56ECh. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - Prob. 62ECh. 6.3 - Prob. 63ECh. 6.3 - Prob. 64ECh. 6.3 - Prob. 65ECh. 6.3 - Prob. 66ECh. 6.3 - Prob. 67ECh. 6.3 - Prob. 68ECh. 6.3 - Prob. 69ECh. 6.3 - Prob. 70ECh. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Prob. 73ECh. 6.3 - Prob. 74ECh. 6.3 - Prob. 75ECh. 6.3 - Prob. 76ECh. 6.3 - Prob. 77ECh. 6.3 - Prob. 78ECh. 6.3 - Prob. 79ECh. 6.3 - Prob. 80ECh. 6.3 - Prob. 81ECh. 6.3 - Prob. 82ECh. 6.3 - Prob. 83ECh. 6.3 - Prob. 84ECh. 6.3 - Prob. 85ECh. 6.3 - Prob. 86ECh. 6.3 - Prob. 87ECh. 6.3 - Prob. 88ECh. 6.3 - Prob. 89ECh. 6.3 - Prob. 90ECh. 6.3 - Prob. 91ECh. 6.3 - Prob. 92ECh. 6.3 - Prob. 93ECh. 6.3 - Prob. 94ECh. 6.3 - Prob. 95ECh. 6.3 - Prob. 96ECh. 6.3 - Prob. 97ECh. 6.3 - Prob. 98ECh. 6.3 - Prob. 99ECh. 6.3 - Prob. 100ECh. 6.3 - Prob. 101ECh. 6.3 - Prob. 102ECh. 6.3 - Prob. 103ECh. 6.3 - Prob. 104ECh. 6.3 - Prob. 105ECh. 6.3 - Prob. 106ECh. 6.3 - Prob. 107ECh. 6.3 - Prob. 108ECh. 6.3 - Prob. 109ECh. 6.3 - Prob. 110ECh. 6.3 - Prob. 111ECh. 6.3 - Prob. 112ECh. 6.3 - Prob. 113ECh. 6.3 - Prob. 114ECh. 6.3 - Prob. 115ECh. 6.3 - Prob. 116ECh. 6.3 - Prob. 117ECh. 6.3 - Prob. 118ECh. 6.3 - Prob. 119ECh. 6.3 - Prob. 120ECh. 6.3 - Prob. 121ECh. 6.3 - Prob. 122ECh. 6.3 - Prob. 123ECh. 6.3 - Prob. 124ECh. 6.3 - Prob. 125ECh. 6.3 - Prob. 126ECh. 6.3 - Prob. 127ECh. 6.3 - Prob. 128ECh. 6.3 - Prob. 129ECh. 6.3 - Prob. 130ECh. 6.3 - Prob. 131ECh. 6.3 - Prob. 132ECh. 6.3 - Prob. 133ECh. 6.3 - Prob. 134ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Prob. 49ECh. 6.4 - Prob. 50ECh. 6.4 - Prob. 51ECh. 6.4 - Prob. 52ECh. 6.4 - Prob. 53ECh. 6.4 - Prob. 54ECh. 6.4 - Prob. 55ECh. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Prob. 59ECh. 6.4 - Prob. 60ECh. 6.4 - Prob. 61ECh. 6.4 - Prob. 62ECh. 6.4 - Prob. 63ECh. 6.4 - Prob. 64ECh. 6.4 - Prob. 65ECh. 6.4 - Prob. 66ECh. 6.4 - Prob. 67ECh. 6.4 - Prob. 68ECh. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - Prob. 71ECh. 6.4 - Prob. 72ECh. 6.4 - Prob. 73ECh. 6.4 - Prob. 74ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.4 - Prob. 77ECh. 6.4 - Prob. 78ECh. 6.4 - Prob. 79ECh. 6.4 - Prob. 80ECh. 6.4 - Prob. 81ECh. 6.4 - Prob. 82ECh. 6.4 - Prob. 83ECh. 6.4 - Prob. 84ECh. 6.4 - Prob. 85ECh. 6.4 - Prob. 86ECh. 6.4 - Prob. 87ECh. 6.4 - Prob. 88ECh. 6.4 - Prob. 89ECh. 6.4 - Prob. 90ECh. 6.4 - Prob. 91ECh. 6.4 - Prob. 92ECh. 6.4 - Prob. 93ECh. 6.4 - Prob. 94ECh. 6.4 - Prob. 95ECh. 6.4 - Prob. 96ECh. 6.4 - Prob. 97ECh. 6.4 - Prob. 98ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - Prob. 49ECh. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Prob. 53ECh. 6.5 - Prob. 54ECh. 6.5 - Prob. 55ECh. 6.5 - Prob. 56ECh. 6.5 - Prob. 57ECh. 6.5 - Prob. 58ECh. 6.5 - Prob. 59ECh. 6.5 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.5 - Prob. 63ECh. 6.5 - Prob. 64ECh. 6.5 - Prob. 65ECh. 6.5 - Prob. 66ECh. 6.5 - Prob. 67ECh. 6.5 - Prob. 68ECh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - Prob. 9ECh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Prob. 12ECh. 6.6 - Prob. 13ECh. 6.6 - Prob. 14ECh. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 6.6 - Prob. 17ECh. 6.6 - Prob. 18ECh. 6.6 - Prob. 19ECh. 6.6 - Prob. 20ECh. 6.6 - Prob. 21ECh. 6.6 - Prob. 22ECh. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Prob. 26ECh. 6.6 - Prob. 27ECh. 6.6 - Prob. 28ECh. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Prob. 33ECh. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Prob. 37ECh. 6.6 - Prob. 38ECh. 6.6 - Prob. 39ECh. 6.6 - Prob. 40ECh. 6.6 - Prob. 41ECh. 6.6 - Prob. 42ECh. 6.6 - Prob. 43ECh. 6.6 - Prob. 44ECh. 6.6 - Prob. 45ECh. 6.6 - Prob. 46ECh. 6.6 - Prob. 47ECh. 6.6 - Prob. 48ECh. 6.6 - Prob. 49ECh. 6.6 - Prob. 50ECh. 6.6 - Prob. 51ECh. 6.6 - Prob. 52ECh. 6.6 - Prob. 53ECh. 6.6 - Prob. 54ECh. 6.6 - Prob. 55ECh. 6.6 - Prob. 56ECh. 6.6 - Prob. 57ECh. 6.6 - Prob. 58ECh. 6.6 - Prob. 59ECh. 6.6 - Prob. 60ECh. 6.6 - Prob. 61ECh. 6.6 - Prob. 62ECh. 6.6 - Prob. 63ECh. 6.6 - Prob. 64ECh. 6.6 - Prob. 65ECh. 6.6 - Prob. 66ECh. 6.6 - Prob. 67ECh. 6.6 - Prob. 68ECh. 6.6 - Prob. 69ECh. 6.6 - Prob. 70ECh. 6.6 - Prob. 71ECh. 6.6 - Prob. 72ECh. 6.6 - Prob. 73ECh. 6.6 - Prob. 74ECh. 6.6 - Prob. 75ECh. 6.6 - Prob. 76ECh. 6.6 - Prob. 77ECh. 6.6 - Prob. 78ECh. 6.6 - Prob. 79ECh. 6.6 - Prob. 80ECh. 6.6 - Prob. 81ECh. 6.6 - Prob. 82ECh. 6.6 - Prob. 83ECh. 6.6 - Prob. 84ECh. 6.6 - Prob. 85ECh. 6.6 - Prob. 86ECh. 6.6 - Prob. 87ECh. 6.6 - Prob. 88ECh. 6.6 - Prob. 89ECh. 6.6 - Prob. 90ECh. 6.6 - Prob. 91ECh. 6.6 - Prob. 92ECh. 6.6 - Prob. 93ECh. 6.6 - Prob. 94ECh. 6.6 - Prob. 95ECh. 6.6 - Prob. 96ECh. 6.6 - Prob. 97ECh. 6.6 - Prob. 98ECh. 6.6 - Prob. 99ECh. 6.6 - Prob. 100ECh. 6.6 - Prob. 101ECh. 6.6 - Prob. 102ECh. 6.6 - Prob. 103ECh. 6.6 - Prob. 104ECh. 6.6 - Prob. 105ECh. 6.6 - Prob. 106ECh. 6.6 - Prob. 107ECh. 6.6 - Prob. 108ECh. 6.6 - Prob. 109ECh. 6.6 - Prob. 110ECh. 6.6 - Prob. 111ECh. 6.6 - Prob. 112ECh. 6.6 - Prob. 113ECh. 6.6 - Prob. 114ECh. 6.6 - Prob. 115ECh. 6.6 - Prob. 116ECh. 6.6 - Prob. 117ECh. 6.6 - Prob. 118ECh. 6.6 - Prob. 119ECh. 6.6 - Prob. 120ECh. 6.6 - Prob. 121ECh. 6.6 - Prob. 122ECh. 6.6 - Prob. 123ECh. 6.6 - Prob. 124ECh. 6.6 - Prob. 125ECh. 6.6 - Prob. 126ECh. 6.6 - Prob. 127ECh. 6.6 - Prob. 128ECh. 6.6 - Prob. 129ECh. 6.6 - Prob. 130ECh. 6.6 - Prob. 131ECh. 6.6 - Prob. 132ECh. 6.6 - Prob. 133ECh. 6.6 - Prob. 134ECh. 6.6 - Prob. 135ECh. 6.6 - Prob. 136ECh. 6.6 - Prob. 137ECh. 6.6 - Prob. 138ECh. 6.6 - Prob. 139ECh. 6.6 - Prob. 140ECh. 6.6 - Prob. 141ECh. 6.6 - Prob. 142ECh. 6.6 - Prob. 143ECh. 6.6 - Prob. 144ECh. 6 - Prob. 1CRCh. 6 - Prob. 2CRCh. 6 - Prob. 3CRCh. 6 - Prob. 4CRCh. 6 - Prob. 5CRCh. 6 - Prob. 6CRCh. 6 - Prob. 7CRCh. 6 - Prob. 8CRCh. 6 - Prob. 9CRCh. 6 - Prob. 10CRCh. 6 - Prob. 11CRCh. 6 - Prob. 12CRCh. 6 - Prob. 13CRCh. 6 - Prob. 14CRCh. 6 - Prob. 15CRCh. 6 - Prob. 16CRCh. 6 - Prob. 17CRCh. 6 - Prob. 18CRCh. 6 - Prob. 19CRCh. 6 - Prob. 20CRCh. 6 - Prob. 21CRCh. 6 - Prob. 22CRCh. 6 - Prob. 23CRCh. 6 - Prob. 24CRCh. 6 - Prob. 25CRCh. 6 - Prob. 26CRCh. 6 - Prob. 27CRCh. 6 - Prob. 28CRCh. 6 - Prob. 29CRCh. 6 - Prob. 30CRCh. 6 - Prob. 31CRCh. 6 - Prob. 32CRCh. 6 - Prob. 33CRCh. 6 - Prob. 34CRCh. 6 - Prob. 35CRCh. 6 - Prob. 36CRCh. 6 - Prob. 37CRCh. 6 - Prob. 38CRCh. 6 - Prob. 39CRCh. 6 - Prob. 40CRCh. 6 - Prob. 41CRCh. 6 - Prob. 42CRCh. 6 - Prob. 43CRCh. 6 - Prob. 44CRCh. 6 - Prob. 45CRCh. 6 - Prob. 46CRCh. 6 - Prob. 47CRCh. 6 - Prob. 48CRCh. 6 - Prob. 49CRCh. 6 - Prob. 50CRCh. 6 - Prob. 51CRCh. 6 - Prob. 52CRCh. 6 - Prob. 53CRCh. 6 - Prob. 54CRCh. 6 - Prob. 55CRCh. 6 - Prob. 56CRCh. 6 - Prob. 57CRCh. 6 - Prob. 58CRCh. 6 - Prob. 59CRCh. 6 - Prob. 60CRCh. 6 - Prob. 61CRCh. 6 - Prob. 62CRCh. 6 - Prob. 63CRCh. 6 - Prob. 64CRCh. 6 - Prob. 65CRCh. 6 - Prob. 66CRCh. 6 - Prob. 67CRCh. 6 - Prob. 68CRCh. 6 - Prob. 69CRCh. 6 - Prob. 70CRCh. 6 - Prob. 71CRCh. 6 - Prob. 72CRCh. 6 - Prob. 73CRCh. 6 - Prob. 74CRCh. 6 - Prob. 75CRCh. 6 - Prob. 76CRCh. 6 - Prob. 77CRCh. 6 - Prob. 78CRCh. 6 - Prob. 79CRCh. 6 - Prob. 80CRCh. 6 - Prob. 81CRCh. 6 - Prob. 82CRCh. 6 - Prob. 83CRCh. 6 - Prob. 84CRCh. 6 - Prob. 85CRCh. 6 - Prob. 86CRCh. 6 - Prob. 87CRCh. 6 - Prob. 88CRCh. 6 - Prob. 89CRCh. 6 - Prob. 90CRCh. 6 - Prob. 91CRCh. 6 - Prob. 92CRCh. 6 - Prob. 93CRCh. 6 - Prob. 94CRCh. 6 - Prob. 95CRCh. 6 - Prob. 96CRCh. 6 - Prob. 97CRCh. 6 - Prob. 98CRCh. 6 - Prob. 99CRCh. 6 - Prob. 100CRCh. 6 - Prob. 101CRCh. 6 - Prob. 102CRCh. 6 - Prob. 103CRCh. 6 - Prob. 104CRCh. 6 - Prob. 105CRCh. 6 - Prob. 106CRCh. 6 - Prob. 107CRCh. 6 - Prob. 108CRCh. 6 - Prob. 109CRCh. 6 - Prob. 110CRCh. 6 - Prob. 111CRCh. 6 - Prob. 112CRCh. 6 - Prob. 113CRCh. 6 - Prob. 114CRCh. 6 - Prob. 115CRCh. 6 - Prob. 116CRCh. 6 - Prob. 117CRCh. 6 - Prob. 118CRCh. 6 - Prob. 119CRCh. 6 - Prob. 120CRCh. 6 - Prob. 121CRCh. 6 - Prob. 122CRCh. 6 - Prob. 123CRCh. 6 - Prob. 124CRCh. 6 - Prob. 125CRCh. 6 - Prob. 126CRCh. 6 - Prob. 127CRCh. 6 - Prob. 128CRCh. 6 - Prob. 129CRCh. 6 - Prob. 130CRCh. 6 - Prob. 131CRCh. 6 - Prob. 132CRCh. 6 - Prob. 133CRCh. 6 - Prob. 134CRCh. 6 - Prob. 135CRCh. 6 - Prob. 136CRCh. 6 - Prob. 137CRCh. 6 - Prob. 138CRCh. 6 - Prob. 139CRCh. 6 - Prob. 140CRCh. 6 - Prob. 141CRCh. 6 - Prob. 142CRCh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 12CTCh. 6 - Prob. 13CTCh. 6 - Prob. 14CTCh. 6 - Prob. 15CTCh. 6 - Prob. 16CTCh. 6 - Prob. 17CTCh. 6 - Prob. 18CTCh. 6 - Prob. 19CTCh. 6 - Prob. 20CTCh. 6 - Prob. 21CTCh. 6 - Prob. 22CTCh. 6 - Prob. 23CTCh. 6 - Prob. 24CTCh. 6 - Prob. 25CTCh. 6 - Prob. 26CTCh. 6 - Prob. 27CTCh. 6 - Prob. 28CTCh. 6 - Prob. 29CTCh. 6 - Prob. 1STPCh. 6 - Prob. 2STPCh. 6 - Prob. 3STPCh. 6 - Prob. 4STPCh. 6 - Prob. 5STPCh. 6 - Prob. 6STPCh. 6 - Prob. 7STPCh. 6 - Prob. 8STPCh. 6 - Prob. 9STPCh. 6 - Prob. 10STPCh. 6 - Prob. 11STPCh. 6 - Prob. 12STPCh. 6 - Prob. 13STPCh. 6 - Prob. 14STPCh. 6 - Prob. 15STPCh. 6 - Prob. 16STPCh. 6 - Prob. 17STPCh. 6 - Prob. 18STPCh. 6 - Prob. 19STPCh. 6 - Prob. 20STPCh. 6 - Prob. 21STPCh. 6 - Prob. 22STPCh. 6 - Prob. 23STPCh. 6 - Prob. 24STPCh. 6 - Prob. 25STPCh. 6 - Prob. 26STPCh. 6 - Prob. 27STPCh. 6 - Prob. 28STP
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