Simplify (2+3i)^2

Problem

(2+3*i)2

Solution

1. Identify the expression as a binomial squared in the form (a+b)2 where a=2 and b=3*i

2. Apply the formula for squaring a binomial: (a+b)2=a2+2*a*b+b2

3. Substitute the values into the formula:

2+2*(2)*(3*i)+(3*i)2

4. Simplify each term individually:

4+12*i+9*i2

5. Recall the definition of the imaginary unit i2=−1 and substitute it into the expression:

4+12*i+9*(−1)

6. Combine the real parts 4 and −9

−5+12*i

Final Answer

(2+3*i)2=−5+12*i

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