How do you simplify #(8-3i)^2#?

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Answer 1 · 2018-08-11T01:23:08

Hope this helps!

#(8-3i)^2#

#(8-3i)(8-3i)#

Use FOIL to distribute/simplify:
#8 * 8 = 64#

#8 * -3i = -24i#

#-3i * 8 = -24i#

#-3i * -3i = 9i^2#

Combine them together:
#64 - 24i - 24i + 9i^2#

Combine like terms:
#64 - 48i + 9i^2#

We know that #i^2 = -1#, so:
#64 - 48i + 9(-1)#

#=64 - 48i - 9#

#=55 - 48i#

Hope this helps!