Question

Express the following in the form of $a+bi$, where $a,b\in R,i=\sqrt{-1}$. State the value of $a$ and $b,\frac{3+2}{2-5i}+\frac{3-2i}{2+5i}$

Answer 1

$i=\sqrt{-1}$

Given,

$\frac{3+2}{2-5i}+\frac{3-2i}{2+5i}$

$=\frac{5}{2-5i}+\frac{3-2i}{2+5i}\times \frac{2-5i}{2-5i}$

$=\frac{5}{2-5i}+\frac{-4-19i}{29}$

$=\frac{5\times 29}{2-5i}+\frac{(-4-19i)\times (2-5i)}{29}$

$=\frac{145+(-103-18i)}{29(2-5i)}$

$=\frac{6(1+i)}{29}$

$=\frac{6}{29}+\frac{6}{29}i=a+ib$

$\therefore a=b=\frac{6}{29}$