Question

The complex number $\frac{1+2i}{1-i}$ lies in which quadrant of the complex plane.

• A. First
• B. Second
• C. Third
• D. Fourth

Answer 1

The correct option is B Second

$\frac{1+2i}{1-i}$

$\Rightarrow \frac{1+2i}{1-i}\times \frac{1+i}{1+i}$

$=\frac{1+i+2i-2i^2}{1-i^2}=\frac{1+3i-2}{2}$

$=\frac{-1+3i}{2}$

$\therefore$ It lies in $2^{nd}$ Quadrant.