How do you multiply #(3+5i)^2 #?

1 Answer
Jun 8, 2016

The answer is #-16+30i#

Explanation:

To square a complex number you do a similar action as if you were to square an expression like #(a+bx)#. The only difference is you have to remember that #i^2=-1#

So:

#(3+5i)^2=3^2+2*3*5i+(5i)^2=9+30i+25i^2#
#=9+30icolor(red)(-25)=9-25+30i=-16+30i#

The minus sign in the marked expression comes from the fact that #i^2=-1#