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Question

Question: If \(z\) is a purely imaginary number, then \(z\) =...

If zz is a purely imaginary number, then zz =

A

3/2

B

1

C

2/3

D

4/9

Answer

1

Explanation

Solution

As given, let =2(x12)+2(y12)+2(x22)+2(y22)=2∣z1∣2+2∣z2∣2= 2(x_{1}^{2}) + 2(y_{1}^{2}) + 2(x_{2}^{2}) + 2(y_{2}^{2}) = 2|z_{1}|^{2} + 2|z_{2}|^{2}or z−1z+1=iy\frac{z - 1}{z + 1} = iy, so that

y∈Ry \in R ⇒\Rightarrow