# How do you divide (4+i)/(2-5i)?

Aug 28, 2016

$\frac{4 + 5 i}{2 - 5 i} = - \frac{17}{29} + \frac{30}{29} i$

#### Explanation:

We should always remember two things while dividing a complex number by another.

One - multiply numerator and denominator each by complex conjugate of the Divisor.

Two - ${i}^{2} = - 1$.

Hence, $\frac{4 + 5 i}{2 - 5 i}$

= ((4+5i)(2+5i))/((2-5i)(2+5i)

= (4×2+4×5i+5i×2+25i^2)/(2×2+2×5i-5i×2-25i^2)

= (8+20i+10i-25)/(4+10i-10i-25×(-1))

= $\frac{- 17 + 30 i}{4 + 25}$

= $\frac{- 17 + 30 i}{29}$

= $- \frac{17}{29} + \frac{30}{29} i$