Simplify (8+9i)^2

Problem

(8+9*i)2

Solution

1. Identify the expression as a binomial square of the form (a+b*i)2 where a=8 and b=9

2. Expand the expression using the binomial expansion formula (a+b)2=a2+2*a*b+b2

(8+9*i)2=8+2*(8)*(9*i)+(9*i)2

3. Calculate the squares and the product of the terms.

(8+9*i)2=64+144*i+81*i2

4. Substitute the value of i2=−1 into the expression.

(8+9*i)2=64+144*i+81*(−1)

5. Simplify the real parts by combining 64 and −81

(8+9*i)2=64−81+144*i

6. Combine the terms to reach the final complex number form a+b*i

(8+9*i)2=−17+144*i

Final Answer

(8+9*i)2=−17+144*i

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