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Find the number of non-zero integral solutions of the equation |1-i|x =2x. - Mathematics

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Question

Find the number of non-zero integral solutions of the equation `|1-i|^x  = 2^x`.

Sum
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Solution

`|1-i|^x  = 2^x`

⇒ `(sqrt(1^2 + (-1)^2))^x = 2^x`

⇒ `(sqrt2)^x  = 2^x`

⇒ `2^(x/2)  = 2^x`

⇒ `x/2  = x`

⇒ x = 2x

⇒ 2x - x = 0

⇒ x = 0

This equation cannot have any solution other than 0.

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Chapter 5: Complex Numbers and Quadratic Equations - Miscellaneous Exercise [Page 113]

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NCERT Mathematics [English] Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Miscellaneous Exercise | Q 18 | Page 113

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