Question

The complex number $\frac{1+2i}{1-i}$ lies in the quadrant :

• A. I
• B. II
• C. III
• D. IV

Answer 1

Answer: (B)

II

Let $z=\frac{1+2i}{1-i}$

$\Rightarrow z=\frac{(1+2i)}{1-i}\times \frac{1+i}{1+i}$

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

$=\frac{1+3i-2}{1+1}$ ............ $[\because i^2=-1]$

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

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

$=x+iy$
Clearly $x<0$ and $y>0$
Hence $z$ lies in $\text{II}$ quadrant