# How do you simplify (8+7i)^2?

Aug 25, 2016

${\left(8 + 7 i\right)}^{2} = 15 + 112 i$

#### Explanation:

Always remember while multiplying or dividing complex numbers that ${i}^{2} = - 1$.

Hence ${\left(8 + 7 i\right)}^{2}$

= 8^2+2×8×7i+(7i)^2

= 64+112i+48+49×(-1)

= $64 - 49 + 112 i$

= $15 + 112 i$