AP EAMCET · Maths · Complex Number
If \(a+b i=\frac{i}{1-i}\), then \((a, b)=\)
- A \(\left(\frac{-1}{2}, \frac{-1}{2}\right)\)
- B \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
- C \(\left(\frac{1}{2}, \frac{-1}{2}\right)\)
- D \(\left(\frac{-1}{2}, \frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{-1}{2}, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & a+b i=\frac{i}{1-i} \\ & \Rightarrow \quad a+b i=\frac{i(1+i)}{2}=-\frac{1}{2}+\frac{i}{2} \\ & \Rightarrow \quad a=-\frac{1}{2}, b=\frac{1}{2} \\ \end{aligned}\)
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