Question

If $ z_{1}=1+2i $ and $ z_{2}=3+5i, $ then $ Re[\bar{z}_{2}z_{1}/z_{2}] $ is equal to

• A. $ -31/17 $
• B. $ 17/22 $
• C. $ -17/31 $
• D. $ 22/17 $

Answer 1

Answer: (D)

We have, $z_{1}=1+2 i$
and $z_{2}=3+5 i$
$\therefore \bar{z}_{2}=3-5 i$
Now, $\bar{z}_{2} z_{1}=(3-5 i)(1+2 i)$
$=3+6 i-5 i-10 i^{2}$
$=3+i+10=13+i$
$\therefore \frac{\bar{z}_{2} z_{1}}{z_{2}}=\frac{(13+i)}{(3+5 i)} \times \frac{(3-5 i)}{(3-5 i)}$
$=\frac{39-65 i+3 i-5 i^{2}}{9+25}$
$=\frac{44-62 i}{34}$
$\therefore $ Real part of $\left(\frac{\bar{z}_{2} z_{1}}{z_{2}}\right)=\frac{44}{34}=\frac{22}{17}$