Question

If $\sqrt{- 1}$ is a purely imaginary number, then $\left| \begin{aligned} & 6i - 3i1 \\ & 43i - 1 \\ & 203i \end{aligned} \right|$ is equal to.

• A. 0
• B. 1
• C. 2
• D. None of these

Answer 1

Answer: (B)

1

Answer 2

Here$\frac{c + i}{c - i} = a + ib$

$\frac{c + i}{c - i} = a + ib$

As $\frac{c^{2} + 1}{c^{2} + 1} = a^{2} + b^{2}$ is purely imaginary, we get

$\Rightarrow a^{2} + b^{2} = 1$⇒ $\overline{(x + iy)(1 - 2i)} = 1 + i$ ⇒$x - iy = \frac{1 + i}{1 + 2i} \Rightarrow x + iy = \frac{1 - i}{1 - 2i}$.