Question 1040428
You're on the right track. You're missing 2 pieces though


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(5 + 7i)^2 is the same as (5 + 7i)*(5 + 7i)


It's like saying x^2 is the same as x*x


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Let's use FOIL to expand out (5 + 7i)*(5 + 7i)


First terms: 5*5 = 25
Inner terms: 7i*5 = 35i
Outer terms: 5*7i = 35i
Last terms: 7i*7i = 49i^2


So we now add up all the terms to get 


25+35i+35i+49i^2


25+70i+49i^2 ... combine like terms


25+70i+49(-1) ... replace i^2 with -1. See note


25+70i-49


-24+70i ... combine like terms



Note: since we have defined i = sqrt(-1), squaring both sides leads to i^2 = -1


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The final answer is -24+70i