Complex Numbers And Quadratic Equations question 827
The number of non-zero integral solutions of the equation $ |1 - i|^{x} = 2^{x} $ is
Options:
A) Finite
1
2
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Since $ 1-i=\sqrt{2}{ \cos \frac{\pi }{4}-i\sin \frac{\pi }{4} },|1-i|=\sqrt{2} $
$ \therefore $ $ |1-i{{|}^{x}}=2^{x} $
Þ $ {{(\sqrt{2})}^{x}}=2^{\frac{x}{2}} $
Þ $ 2^{x/2} = 2^{x} $
Þ $ \frac{x}{2}=x $
Þ $ x=0 $ Therefore, the number of non-zero integral solutions is nil or zero.
BETA
