Question 529800


{{{(1+2i)*(1-2i)}}} Start with the given expression.



{{{(1)(1)+(1)(-2i)+(2i)(1)+(2i)(-2i)}}} FOIL.



{{{1-2i+2i-4i^2}}} Multiply.



{{{1-2i+2i-4(-1)}}} Replace {{{i^2}}} with {{{-1}}}. Note: {{{i^2=-1}}}.



{{{1-2i+2i+4}}} Multiply.



{{{5+0i}}} Combine like terms.



{{{5}}} Simplify



So {{{(1+2i)*(1-2i)=5}}}.



The expression is now in standard form {{{a+bi}}} where {{{a=5}}} and {{{b=0}}} 



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