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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $1$
B $0$
C $2$
D $3$

Correct answer: A

Solution

(a) | 1 - i | (1)^{2} + (- 1)^{2} = 2 ∴ | 1 - i |^{x} = 2^{x} \Rightarrow (2)^{x} = 2^{x} \Rightarrow 2^{x /2} = 2^{x} ∴ \frac{x}{2} = x only possible if x = 0 ∴ Number of integer solution = 1

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