How do you multiply out #(1- 2i ) ^ { 3}#?

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Answer 1 · 2017-06-06T19:55:32

#-11+2i#

In two stages:

#color(brown)("Stage 1: "->" "(1-2i)^2)#

#color(green)(color(blue)((1-2i))(1-2i))#

#color(green)(color(blue)(1)(1-2i)color(blue)(-2i)(1-2i)) #

#1-2i-2i+4(i)^2#

#1-4i-4#

#-3-4i#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Stage 2: "->" "(1-2i)(1-2i)^2)#

#color(green)(color(blue)((1-2i))(-3-4i))#

#color(green)(color(blue)(1)(-3-4i)color(blue)(-2i)(-3-4i) )#

#-3-4i+6i+8(i)^2#

#-3+2i-8#

#-11+2i#