Question

If $|z| - z = 1 + 2i$and $2 - \frac{3}{2}i$then $\frac{3}{2} + 2i$ is.

• A. Purely real
• B. Purely imaginary
• C. Zero
• D. Undefined

Answer 1

Answer: (B)

Purely imaginary

Answer 2

$(z_{1}) - arg(z_{2}) = 0$ .....(i)

Now, $|z_{1} + z_{2}| = |z_{1}| + |z_{2}| \Rightarrow z_{1},z_{2}$

$\therefore argz_{1} = argz_{2} \Rightarrow argz_{1} - argz_{2} = 0z = 5 - \sqrt{3}i$ [by equation (i)]

Hence, $r(\cos\theta + i\sin\theta) = 5 - \sqrt{3}i$is purely imaginary.