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

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

4. Substitute the value of i^2=−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

Want more problems? Check here!