A) \[{{\alpha }^{2}}-{{\beta }^{2}}=-1\]
B) \[{{\alpha }^{2}}-{{\beta }^{2}}=1\]
C) \[{{\alpha }^{2}}+{{\beta }^{2}}=1\]
D) \[{{\alpha }^{2}}-{{\beta }^{2}}=2\]
Correct Answer: C
Solution :
\[\alpha -i\beta =\frac{3-4xi}{3+4xi}\]. Taking modulus and squaring on both sides, \[{{\alpha }^{2}}+{{\beta }^{2}}=1\].
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