AP EAMCET · Maths · Complex Number
If \(u+i v=\frac{3 i}{x+i y+2}\), then \(y=\)
- A \(\frac{9 u}{u^2+v^2}\)
- B \(\frac{3 u}{u^2+v^2}\)
- C \(\frac{6 u}{u^2+v^2}\)
- D \(\frac{12 u}{u^2+v^2}\)
Answer & Solution
Correct Answer
(B) \(\frac{3 u}{u^2+v^2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {We have, } u+i v=\frac{3 i}{x+i y+2} \\ & \Rightarrow x+i y+2=\frac{3 i}{u+i v} \\ & \Rightarrow(x+2)+i y=\frac{3 i}{u+i v}+\frac{u-i v}{u-i v}=\frac{3 u i-3 v\left(i^2\right)}{u^2-(i v)^2} \\ & \Rightarrow(x+2)+i y=\frac{3 u i+3 v}{u^2+v^2} \\ &…
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