Find zw and . Write each answer in polar form and in exponential form. 2т z = COs 3 +i sin 27 and 57 + i sin 9. 57 W = COS 11T 11T Zw = coS + i sin 7 11T or e 7 E + i sin = COS or 11T 11T +i sin 9. 11T Zw = COS or e 9 ||

Q: 6. Write [2(cos15°+isin15°)J in rectangular form. (c) 4+4i (d) 4/7 + 4i/7 (a) 3+3i (b) 3/2 + 3i/7

A: Distribute the exponent 3, then for the polar part 3 will multiply with the angles.

Q: Perform the necessary operations to solve the following. Given z1 = 2 + 4i Z2 = 5e2i Z3 = 4 cis 40°…

A: To write the necessary operations.

Q: Find zw and z/w. Write each answer in exponential and polar form. z = 6 ( cos pi/10 + i sin pi/10 )…

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Q: Let z = 7 (cos (7π/9) + i sin (7π/9))  and w = 6 (cos (2π/3) + i sin (2π/3)).  If zw is expressed…

A: Introduction: A complex number has many different representations. These are the rectangular…

Q: - . Write cos(i – 4) in the form of a + bi.

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Q: We have 27 Cos (u) du= and converting back to an expression in X qrues us

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Q: 2. Find the cartesian equation of the following: а. r = 3-sin e b. r? cos(20) = 4 9. r2 C. 4 sin(26)

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Q: Find the quotient where z1 and z2 are given Z2 below. zi = 24 (cos(171°) + i sin(171°)) Z2 = 4…

A: z1=24(cos171°+isin171°)=24ei171°z2=4(cos51°+isin51°)=4ei51°

Q: B)Convert r = √2 cos (0-) to cartesian.

A: we need to convert polar coordinate into cartesian.

Q: 21 = 4 cos + i sin and z2 = 2 + i sin Compute the following, and put the result in a + bi form where…

A:

Q: Find the four fourth roots of  z = 81(cos 4pi/3 + i sin 4pi/3) w0=  w1= w2= w3= .  Write each…

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Q: 16. Express the quotient 00. √3 5 O b. √3 1 OC. √3 6 O d. √3 2 1 3(cos50°+isin50°),…

A: Topic:- complex number

Q: Express in the form a + bi where a and b are real numbers.

A: we have z = 12cos4π3+ isin4π3    Now 4π3= π+π3 hence z = 12cosπ+π3+ isinπ+π3               =…

Q: Find zw and W Write each answer in polar form and in exponential for - Z=7| cos + i sin 4 4 兀 W =7|…

A: use product of complex numbers in polar form zw=r1r2[cos(θ1+θ2)+ isin(θ1+θ2)]   use product of…

Q: Find zw and Write each answer in polar form and in exponential form. W |- 27 Z = 2 cos -+i sin 6. w…

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Q: B)Convert r = √2 cos(0-) to cartesian.

A:

Q: If z = 1+ 2i and w 3+ 4i, express in rectangular form 5 cos [Arg (2²)] + 5i sin[Arg w]

A: The square of a complex number z is the product of z with itself. Multiply 1+2i by 1+2i to obtain…

Q: 5. Z=2(cos9°+isin9°) find Z and write in the form a+bi.

A:

Q: Find the product of z1 & Z2, leave answer in trigonometric form: 235 (cos플 + isin) & z2 =: +i sin 3…

A: We know that for  z1 = r1 cos θ1 + i sin θ1  and  z2 = r2 cos θ2 + i sin θ2 z1·z2 = r1·r2 cosθ1+θ2 +…

Q: 1. Simplify (cos(4L25°) – tanh (0.3 + j0.7) cosh (In (3 + j5)(3+j5)) and write your final answer in…

A: Given expression is coshcos4∠25°-tanh0.3+j0.7ln3+j53+j5

Q: Express each of the following numbers in polar form (reje, with in radians) without using a…

A:

Q: Write z = 4(cos 120° + isin 120°) in rectangular form, a + bi.

A: z=4cos120°+isin120°

Q: Find cos Co + u given that COs o =) se3z and cos =3. and that & and 4 are between O and /2.

A: Follow the steps.

Q: Express in the form a + bi, where a and b are real numbers.

A: 20cos11π6+ i sin11π6

Q: Find zw and . Write each answer in polar form and in exponential form. cos 4 +i sin2 and 뚱 + i sin…

A:

Q: 3. Simplify the following, giving the results in polar form (1) 3(cos 143° + j sin 143°) X 4(cos 57°…

A: Cos(x)+isin(x)=e^(ix) Please see the explanation below

Q: z=16(cos90+isin90) z=4(cos60+isin60) find z1/z2 and write in the form a+bi

A:

Q: Find the product z,z2 and the quotient 1. Express your answers in polar form. 21 = 7(co() + i sin ),…

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Q: Evaluate by Wallis's Formula. Show the complete solution. S cos 30 de

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Q: Find only five of the following: 1-[t? cos at 2-(6 sin 2t – 5 cos 2t ) |

A: as per the guidelines of the company we need to solve the first 3 subparts of a question ,as the…

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: To find The roots of the given complementary solution.

Q: Express the following in polar form): (iii) (cos 300° + i sin 30"). 2 i) sin 60° + i cos 60° (ii)…

A:

Q: Find the four fourth roots of z = 256( cos 21 + i sin 3 Write each root in standard form. 3 Wo =…

A: The given question can be solved as shown in step2.

Q: Find zw and Write each answer in polar form and in exponential form. Z= 2| cos +i sin 3 w = 2 cos +…

A:

Q: Given that z = 1- iv3, express z in the form r(cos 0 +i sin 0). Hence write down z' in the form…

A:

Q: Find the points of intersection of r = 1 andr = 1+2 cos 0.

A: General solution of cosθ = cosα is                           θ = 2nπ ±α

Q: Find zw and Write each answer in polar form and in exponential form. W Z= 6 cos -+i sin 5. W = 6 cos…

A:

Q: d. Use the compound angle formulae to expand x1 and x2 into the form A sin 100nt + B cos 100nt,…

A: Displacement caused by the vibration of beam is modelled by the equations x1=3.75sin100πt+2π9…

Q: a) Let zi = 4 cos Find 2₁ - 22 and 7π 12 21 Z2 5TT 12 + i sin and = 3 (cos. Leave your answer in…

A:

Q: (1) I= 3 Cos 2x do dx 1+51n2

A:

Q: (b) If cos (20) = 3/5 and 0 <0 ST/4, find the values of i. sin (20) %3D ii. cos (0) iii. sin (0)

A: If the angle belongs to  0≤θ≤π4, then 2θ belongs to0≤2θ≤π2          It means 2θ is in quadrant I…

Q: 6. Find cos(u + u) and simplify as much as possible.

A: Find cosu+u and simplify as much as possible.

Q: Let z1 = 4(cos 80° + i sin 80°) and z2 = 6(cos 145° + i sin 145°). Find the product z1z2 and write…

A: cos80° = 0.17sin80° = 0.98cos145° = -0.82sin145° = 0.57

Q: Find u to the nearest tenth of a degree if 0 &lt;= u &lt; 360°,        cos u = 0.2351

A: cos u = 0.2351 cos is positive in first and fourth quadrant. So if x is the angle in first quadrant,…

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: We will find out the required roots of given complementary solution.

Q: 1. Find (2r - e") dr 2. Find 3er da 3. Find (r+ cos 2r) dr

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Which of the following are solutions to the following equation where 0 < 0 < 2n 2 cos(30) = -V2 %3D

A: Given

Q: 7 Tt 2a) Find cos 6.

A:

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: The given complementary solution is y=(c1+c2x)cos2x+(c3+c4x)sin2x

Q: Given z, = 18(cos 175°+i sin 175º ) dan z, = 6(cos 54°+i sin 54°). Find: i. ii.

A: