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TS EAMCET · Maths · Complex Number

Let \(z=a-\frac{i}{2} ; a \in R\). Then \(|i+z|^2-|i-z|^2\) is equal to

  1. A 2
  2. B -2
  3. C 4
  4. D -4
Verified Solution

Answer & Solution

Correct Answer

(B) -2

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Given, } z=a-\frac{i}{2} \\ & \begin{aligned} & \therefore|i+z|^2-|i-z|^2=\left|a+\frac{i}{2}\right|^2-\left|-a+\frac{3 i}{2}\right|^2 \\ &=a^2+\left(\frac{1}{2}\right)^2-\left(a^2+\left(\frac{3}{2}\right)^2\right) \\…