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

Problem

(2+3*i)*(2−3*i)

Solution

1. Identify the expression as a product of two binomials in the form (a+b*i)*(a−b*i) which represents the product of complex conjugates.

2. Apply the FOIL method or the difference of squares formula (a+b)*(a−b)=a2−b2

3. Substitute the values a=2 and b=3*i into the formula.

2−(3*i)2

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

4−9*i2

5. Recall the definition of the imaginary unit, where i2=−1

4−9*(−1)

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

4+9

13

Final Answer

(2+3*i)*(2−3*i)=13

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