TS EAMCET · Maths · Complex Number
If the conjugate of \((x+i y)(1-2 i)\) is \((1+i)\), then
- A \(x+i y=1-i\)
- B \(x+i y=\frac{1-i}{1-2 i}\)
- C \(x-i y=\frac{1-i}{1+2 i}\)
- D \(x-i y=\frac{1-i}{1+i}\)
Answer & Solution
Correct Answer
(B) \(x+i y=\frac{1-i}{1-2 i}\)
Step-by-step Solution
Detailed explanation
We have, Conjugate of \((x+i y)(1-2 i)\) is \(1+i\). i.e. \(\quad(x-i y)(1+2 i)=1+i\) \(\Rightarrow \quad x-i y=\frac{1+i}{1+2 i}\) Taking conjugate both sides, we get \[ x+i y=\frac{1-i}{1-2 i} \]
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