Question 4, Review Exercise

Solutions of Question 4 of Review Exercise of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Locate the complex number z=x+iy on the complex plane if |z+2iz2i|=1

Solution.

Given z=x+iy, then |z+2iz2i|=1|z+2i|=|z2i||x+i(y+2)|=|x+i(y2)|x2+(y+2)2=x2+(y2)2 Squaring both sides, we have x2+(y+2)2=x2+(y2)2(y+2)2=(y2)2y2+4y+4=y24y+44y+4y=08y=0y=0. Hence, we conclude z=x+i0 z=x.