# How do you simplify # (2+5i)^2#?

##### 1 Answer

Jan 27, 2016

#### Explanation:

First, distribute this using FOIL as you normally would a binomial.

#(2+5i)^2=(2+5i)(2+5i)=#

#overbrace(2xx2)^("First")+overbrace(2xx5i)^"Outside"+overbrace(5ixx2)^"Inside"+overbrace(5ixx5i)^"Last"#

This gives

#4+10i+10i+25i^2#

or

#4+20i+25i^2#

While this may look simplified, we can go one step further.

Since

#4+20i+25(-1)#

Now, subtract the

#-21+20i#