Simplify (7+8i)^2

Problem

(7+8*i)^2

Solution

1. Identify the expression as a binomial square of the form (a+b)^2 where a=7 and b=8*i

2. Apply the formula for squaring a binomial: (a+b)^2=a^2+2*a*b+b^2

3. Substitute the values into the formula:

(7+8*i)^2=7^2+2*(7)*(8*i)+(8*i)^2

4. Calculate the squares and the product:

7^2=49

2*(7)*(8*i)=112*i

(8*i)^2=64*i^2

5. Apply the property of the imaginary unit where i^2=−1

64*i^2=64*(−1)=−64

6. Combine the real parts and the imaginary part:

49+112*i−64

(49−64)+112*i

−15+112*i

Final Answer

(7+8*i)^2=−15+112*i

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