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

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Answer 1 · 2018-08-13T03:40:04

#21 - i#

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

Use FOIL to distribute/expand:
#2 * 3 = 6#

#2 * -5i = -10i#

#3i * 3 = 9i#

#3i * -5i = -15i^2#

Combine them together:
#6 - 10i + 9i - 15i^2#

Combine like terms:
#6 - i - 15i^2#

We know that #i^2 = -1#, so:
#6 - i - 15(-1)#

#=6 - i + 15#

#=21 - i#

Hope this helps!