The number of non-zero integral solutions of the equation | 1 − i | x = 2 x is Options: A . &nbspzero B . &nbsp1 C . &nbsp2 D . &nbspNone 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=2x

Question

The number of non-zero integral solutions of the equation

| 1 - i |^{x}

2^{x}

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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