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

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Answer 1 · 2018-07-28T12:56:16

#16-30i#

Given that

#(5-3i)^2#

#=(5-3i)(5-3i)#

#=25-15i-15i+9i^2#

#=25-30i-9#

#=16-30i#

Answer 2 · 2018-07-28T12:56:38

#color(indigo)(=> 16 - 30 i#

#(a - b)^2 = a^2 - 2ab + b^2#, identity.

#(5- 3 i)^2 = 5^2 - (2*5*3 i) + (3 i)^2#

#i^2 = -1#

#=> 25 - 30 i - 9#

#=> 25 - 9 - 30 i#

#color(indigo)(=> 16 - 30 i#