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

1 Answer
Jun 19, 2018

#12-8i#

Explanation:

Like we would do with real numbers, we can multiply this out with FOIL (Firsts, Outsides, Insides, Lasts). This is the order we multiply in. We get

  • First terms: #-5*-2=10#
  • Outside terms: #-5*2i=-10i#
  • Inside terms: #-i*-2=2i#
  • Last terms: #-i*2i=-2i^2#

This leaves us with

#-2i^2-10i+2i+10#

Which can be simplified further as

#-2i^2-8i+10#

Note that #i^2=-1#, so we can plug in this value. We now have

#-2(-1)-8i+10#

Which finally simplifies to

#12-8i#

Hope this helps!