Simplify (3-2i)^2

Problem

(3−2*i)2

Solution

1. Identify the expression as a binomial square of the form (a−b)2 where a=3 and b=2*i

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

3. Substitute the values into the formula:

(3)2−2*(3)*(2*i)+(2*i)2

4. Evaluate each term individually:

3=9

−2*(3)*(2*i)=−12*i

(2*i)2=4*i2

5. Apply the property of the imaginary unit where i2=−1

4*i2=4*(−1)=−4

6. Combine the real parts and the imaginary part:

9−12*i−4

9−4−12*i

5−12*i

Final Answer

(3−2*i)2=5−12*i

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