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.
Question 4
Locate the complex number z=x+iy on the complex plane if |z+2iz−2i|=1
Solution.
Given z=x+iy, then |z+2iz−2i|=1⟹|z+2i|=|z−2i|⟹|x+i(y+2)|=|x+i(y−2)|⟹√x2+(y+2)2=√x2+(y−2)2 Squaring both sides, we have x2+(y+2)2=x2+(y−2)2⟹(y+2)2=(y−2)2⟹y2+4y+4=y2−4y+4⟹4y+4y=0⟹8y=0⟹y=0. Hence, we conclude z=x+i⋅0 ⟹z=x.
Go to