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#