The number of non-zero integral solutions of the equation | 1 − i | x = 2 x is Options: A . &nbsp zero B . &nbsp 1 C . &nbsp 2 D . &nbsp None of these

Answer: Option A : A Since1-i = √ 2 [ c o s π 4 − i s i n π 4 ] , |1-i| ∴ | 1 − i | x = 2 x ⇒ ( √ 2 ) x = 2 x ⇒ 2 x / 2 = 2 x ⇒ x 2 =x then x=0. Therefore, the number of non-zero integral solutions is nil or Zero.

The number of non-zero integral solutions of the equation |1−i|x=

Question

The number of non-zero integral solutions of the equation $| 1 - i |^{x}$ = $2^{x}$ is

Options:

A . zero

B . 1

C . 2

D . None of these

Answer: Option A
:
A

Since1-i = $\sqrt{2}$ $[c o s \frac{π}{4} - i s i n \frac{π}{4}]$ , |1-i|

$∴$ $| 1 - i |^{x}$ = $2^{x}$ $\Rightarrow$ ${(\sqrt{2})}^{x}$ = $2^{x}$ $\Rightarrow$ $2^{x / 2}$ = $2^{x}$

$\Rightarrow$ $\frac{x}{2}$ =x then x=0.

Therefore, the number of non-zero integral solutions is nil or Zero.

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