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=a^2+2*a*b+b^2

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

3. Calculate the squares and the product.

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

4. Substitute i^2=−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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