Question
Asked Oct 26, 2019

Hi, the question is attached! 

I only need part iii), so don't worry about i) and ii) !!!!

Thanks ? 

Question 8
(i) If z cos 0 + i sin 0 , show that 1 +z = 2 cos (cOS+ i sin)
ө
ө
2
(ii) z1, Z2 are complex numbers such that Iz,1l | z 2l = 1. If z1, Z2 have arguments
a and B
cos
2
respectively, where -T < a
< m and -n <BT, show that
Z1+Z1Z2
has modulus
and argument
Z1+1
COS
2
a+p
2
(iii) |z,=| z2l
1 and
22i. Find z1 and z2in the form of x + iy
Z1+1
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Question 8 (i) If z cos 0 + i sin 0 , show that 1 +z = 2 cos (cOS+ i sin) ө ө 2 (ii) z1, Z2 are complex numbers such that Iz,1l | z 2l = 1. If z1, Z2 have arguments a and B cos 2 respectively, where -T < a < m and -n <BT, show that Z1+Z1Z2 has modulus and argument Z1+1 COS 2 a+p 2 (iii) |z,=| z2l 1 and 22i. Find z1 and z2in the form of x + iy Z1+1

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Expert Answer

Step 1

To determine the complex numbers z and w (change notation to avoid suffixes) satisfying the given conditions

Step 2

From (ii), set up equations f...

ii)From ()
1.| w |=1 and
= 2i
1
cos
2
2 (:1 2i 2)
(1)and
-
cos
2
arg(2)=(2)
2
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ii)From () 1.| w |=1 and = 2i 1 cos 2 2 (:1 2i 2) (1)and - cos 2 arg(2)=(2) 2

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