Complex Numbers And Quadratic Equations question 81
Question: A real value of x will satisfy the equation $ ( \frac{3-4ix}{3+4ix} )= $ $ \alpha -i\beta (\alpha ,\beta \text{real),} $ if [Orissa JEE 2003]
Options:
A) $ {{\alpha }^{2}}-{{\beta }^{2}}=-1 $
B) $ {{\alpha }^{2}}-{{\beta }^{2}}=1 $
C) $ {{\alpha }^{2}}+{{\beta }^{2}}=1 $
D) $ {{\alpha }^{2}}-{{\beta }^{2}}=2 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \alpha -i\beta =\frac{3-4xi}{3+4xi} $ . Taking modulus and squaring on both sides, $ {{\alpha }^{2}}+{{\beta }^{2}}=1 $ .
BETA
