Question 73647
Given:
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{{{(-1+i)^2 }}}
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Squaring this quantity means to multiply it by itself.  So let's re-write this as a multiplication
problem:
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{{{(-1+i)*(-1+i)}}}
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We can do this as a FOIL multiplication (multiply Firsts, Outsides, Insides and Lasts) and 
add all the results together to get the answer.
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Multiply the first terms in each set of parentheses gives -1 times -1 and the result is +1.
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Next multiply the outside terms in each set gives -1 times +i = -i.
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Next multiply the inside terms in each set gives i times -1 = -i.
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Finally multiply the last terms in each set to get {{{i*i = i^2}}}. But recall the definition
of {{{i^2}}} It is that i squared = -1, so in this case we replace this product by -1.
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Now add all four results together:
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+1 -i -i - 1
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The +1 and -1 cancel each other, and the two -i terms add to become -i*2 which is the 
answer to this problem. (or -2*i if that's the order in which your lessons put it.)
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Hope this helps you to understand multiplication of complex numbers a little better.