How do you simplify #(-1+6i)^2#?

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Answer 1 · 2018-08-10T17:52:37

#37 - 12i#

#(-1+6i)^2#

#(-1+6i)(-1+6i)#

Use FOIL to distribute:
#-1 * -1 = 1#

#-1 * 6i = -6i#

#6i * -1 = -6i#

#6i * -6i = -36i^2#

Combine them all together:
#1 - 6i - 6i - 36i^2#

Combine like terms:
#1 - 12i - 36i^2#

We know that #i^2# = -1#, so: #1 - 12i - 36(-1)#

#1 - 12i + 36#

Simplify:
#37 - 12i#

Hope this helps!