Q157 / 270 · NDA 2015 (Phase 2) · Mathematics

If $z_1$ and $z_2$ are complex numbers with $\left|z_1\right|=\left|z_2\right|$, then which of the following is/are correct? 1. $\mathrm{z}_1=\mathrm{z}_2$ 2. Real part of $z_1=$ Real part of $z_2$ 3. Imaginary part of $z_1=$ Imaginary part of $z_2$ Select the correct answer using the code given below :

  • A
    1 only
  • B
    2 only
  • C
    3 only
  • Correct answer
    D
    None

Solution

$\begin{aligned} & \text { Let } Z_1=a_1+i b_1 \\ & Z_2=a_2+i b_2 \\ & \left|Z_1\right|=\left|Z_2\right| \\ & \sqrt{\left(a_1\right)^2+\left(b_1\right)^2}=\sqrt{\left(a_2\right)^2+\left(b_2\right)^2} \end{aligned}$ It is true for many values of $a_1, a_2 \& b_1, b_2$. So $a_1$ must not equal to $\mathrm{a}_2$, and $\mathrm{b}_1$ must not equal to $\mathrm{b}_2$.

Hence, the correct answer is option: 'D'.

Relevant Questions