Question

Find $\frac{z_1}{z_2}$, when $z_1=6+2i$ and $z_2=2-i$.

• (A) $(1+i)$
• (B) $2(1+i)$
• (C) $2+i$
• (D) $(1-i)$

Answer 1

The Correct Option is B

Explanation:
Given,$z_1=6+2i$...(1)  $z_2=2-i$...(2)On dividing equation (1) and (2), we get$\frac{z_1}{z_2}=\frac{6+2i}{2-i}$Multiplying by $(2+i)$ in numerator and denominator, we get$\frac{z_1}{z_2}=\frac{6+2i}{2-i}\times \frac{2+i}{2+i}$$\Rightarrow \frac{z_1}{z_2}=\frac{12+6i+4i+2i^2}{2^2-i^2}$$\Rightarrow \frac{z_1}{z_2}=\frac{12+10i+2\times (-1)}{4-(-1)}[\because i^2=-1]$$\Rightarrow \frac{z_1}{z_2}=\frac{12+10i-2}{4+1}$$\Rightarrow \frac{z_1}{z_2}=\frac{10+10i}{5}$$\Rightarrow \frac{z_1}{z_2}=\frac{10(1+i)}{5}$$\Rightarrow \frac{z_1}{z_2}=2(1+i)$Hence, the correct option is (B).