Simplify (3+2i)(3-2i)

Problem

(3+2*i)*(3−2*i)

Solution

1. Identify the expression as a product of conjugates in the form (a+b*i)*(a−b*i)

2. Apply the formula for the difference of squares, which states (x+y)*(x−y)=x2−y2

3. Substitute x=3 and y=2*i into the formula.

3−(2*i)2

4. Evaluate the squares of the real and imaginary parts.

9−4*i2

5. Substitute i2=−1 into the expression.

9−4*(−1)

6. Simplify the arithmetic to find the final real number.

9+4

13

Final Answer

(3+2*i)*(3−2*i)=13

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