TS EAMCET · Maths · Complex Number
If \(\mathrm{x}+\mathrm{iy}=\sqrt{\frac{3+i}{1+3 i}}\), then \(\left(x^2+y^2\right)^2=\)
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & x+i y=\sqrt{\frac{3+i}{1+3 i}}=\sqrt{\frac{(3+i)}{(1+3 i)} \times \frac{(1-3 i)}{(1-3 i)}} \\ &= \sqrt{\frac{6-8 i}{10}}=\sqrt{\frac{3}{5}-\frac{4}{5} i} \\ & \therefore \quad(x+i y)^2=\frac{3}{5}-\frac{4}{5} i \\ & \Rightarrow \quad x^2-y^2+2 x y…
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