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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

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.5: Trigonometric Form For Complex Numbers
Problem 20E
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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
Transcribed Image Text: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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