If $a+b i=\frac{i}{1-i}$, then $(a, b)=$

Question

Aicharya · Accepted Answer

$\begin{aligned} & a+b i=\frac{i}{1-i} \ & \Rightarrow \quad a+b i=\frac{i(1+i)}{2}=-\frac{1}{2}+\frac{i}{2} \ & \Rightarrow \quad a=-\frac{1}{2}, b=\frac{1}{2} \ \end{aligned}$

If \(a+b i=\frac{i}{1-i}\), then \((a, b)=\)

Solution