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...

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

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

Extracted 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="">

Jun 03, 2022

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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...

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