a+i b form of the complex number 1+3 i 2+3 i is - Vidyadip

MCQ

$a+i b$ form of the complex number $\frac{1+3 i}{2+3 i}$ is

A
$\frac{3}{13}+i \frac{11}{13}$
✓
$\frac{11}{13}+ i \frac{3}{13}$
C
$\frac{2}{11}+ i \frac{3}{11}$
D
$\frac{2}{11}- i \frac{3}{11}$

✓

Answer

Correct option: B.

$\frac{11}{13}+ i \frac{3}{13}$

(B)
$\frac{1+3 i}{2+3 i}=\frac{(1+3 i)(2-3 i)}{(2+3 i)(2-3 i)}=\frac{2+3 i+9}{4+9}$
$=\frac{11}{13}+\frac{3}{13} i$

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