Question

If $(1,2)$ and $( - 1, - 2)$ are two complex numbers satisfying the equation $\frac{2 + 5i}{4 - 3i}$=1, then $\frac{7 - 26i}{25}$ is a number which is.

• A. Positive real
• B. Negative real
• C. Zero or purely imaginary
• D. None of these

Answer 1

Answer: (C)

Zero or purely imaginary

Answer 2

Given $\sqrt{x^{2} + y^{2}} - x = 1$⇒ $y = - 2$ (say)

⇒ $x = \frac{3}{2}$

which is zero, if $z = \frac{3}{2} - 2i$ and is otherwise purely imaginary.