How do you simplify #(-2+5i)(-1+4i)#?

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Answer 1 · 2018-08-10T17:55:25

#-18 - 13i#

#(-2*5i)(-1+4i)#

Use FOIL to distribute:
#-2 * -1 = 2#

#-2 * 4i = -8i#

#5i * -1 = -5i#

#5i * 4i = 20i^2#

Combine them together:
#2 - 8i - 5i + 20i^2#

Combine like terms:
#2 - 13i + 20i^2#

We know that #i^2 = -1#, so:
#2 - 13i + 20(-1)#

#2 - 13i - 20#

Simplify:
#-18 - 13i#

Hope this helps!