For any complex number (x + iy = \frac{1 - i}{1 - 2i})if and... | MATH - CONJUGATE, MODULUS AND ARGUMENT OF COMPLEX NUMBERS | SolveeIt

For any complex number $x + iy = \frac{1 - i}{1 - 2i}$ if and only if.

$x - iy = \frac{1 - i}{1 + 2i}$ is a pure real number

$\frac{(2 + i)^{2}}{3 + i},$

$\frac{13}{2} + i\left( \frac{15}{2} \right)$ is a pure imaginary number

$\frac{13}{10} + i\left( \frac{- 15}{2} \right)$

Answer

$\frac{(2 + i)^{2}}{3 + i},$

Explanation

Given that

$iz_{1} = - \left( \cot\frac{\alpha}{2} \right)z_{2}$ ⇒ $iz_{1} = kz_{2}$ .

Question: For any complex number \(x + iy = \frac{1 - i}{1 - 2i}\)if and only if....