Simplify (3+4i)(3-4i)

Problem

(3+4*i)*(3−4*i)

Solution

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

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

3. Substitute the values into the formula:

3−(4*i)2

4. Evaluate the squares:

9−16*i2

5. Substitute the definition of the imaginary unit i2=−1

9−16*(−1)

6. Simplify the arithmetic:

9+16=25

Final Answer

(3+4*i)*(3−4*i)=25

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