How do you simplify #(5-7i)(-4-3i)#?

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Answer 1 · 2018-08-10T17:54:06

#-41 + 13i#

#(5-7i)(-4-3i)#

Use FOIL to distribute:
#5 * -4 = -20#

#5 * -3i = -15i#

#-7i * -4 = 28i#

#-7i * -3i = 21i^2#

Combine them all together:
#-20 - 15i + 28i + 21i^2#

Combine like therms:
#-20 + 13i + 21i^2#

We know that #i^2 = -1#, so:
#-20 + 13i + 21(-1)#

#-20 + 13i - 21#

#-41 + 13i#

Hope this helps!