Simplify (6+7i)^2

Problem

(6+7*i)2

Solution

1. Identify the expression as a binomial square of the form (a+b*i)2 where a=6 and b=7

2. Expand the expression using the identity (a+b)2=a2+2*a*b+b2

(6+7*i)2=6+2*(6)*(7*i)+(7*i)2

3. Calculate the squares and the product.

(6+7*i)2=36+84*i+49*i2

4. Substitute i2=−1 into the expression.

(6+7*i)2=36+84*i+49*(−1)

5. Simplify the real terms by combining 36 and −49

36−49=−13

6. Combine the results into the final complex form a+b*i

−13+84*i

Final Answer

(6+7*i)2=−13+84*i

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