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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 50 of 52
Marks: +1, -0
Find the number of non-zero integral solutions of the equation ∣1−i∣x|1-i|^x = 2x2^x
Solution:  
∣1−i∣x|1-i|^x = 2x2^x , (1+1)x(\sqrt{1+1})^x = 2x2^x ⇒ (2)x(\sqrt{2})^x = 2x2^x
⇒ (21/2)x(2^{1/2})^x = 2x2^x ⇒ 2x/22^{x/2} = 2x2^x ⇒ x2\frac{x}{2} = x ⇒ 2x = x ⇒ x = 0
∴ The number of non-zero integral solutions is 0.
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