How do you simplify #(5 – 3i)(2 + 4i)#?

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Answer 1 · 2018-08-14T03:55:48

#22 + 14i#

#(5-3i)(2+4i)#

Use FOIL to distribute/expand:
#5 * 2 = 10#

#5 * 4i = 20i#

#-3i * 2 = -6i#

#-3i * 4i = -12i^2#

Combine them together:
#10 + 20i - 6i - 12i^2#

Simplify:
#10 + 14i - 12i^2#

We know that #i^2 = -1#, so:
#10 + 14i - 12(-1)#

Simplify:
#10 + 14i + 12#

#22 + 14i#

Hope this helps!