Simplify (2+7i)(2-7i)

Problem

(2+7*i)*(2−7*i)

Solution

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

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

3. Expand the terms to get 2^2−(7*i)^2

4. Calculate the squares of the real and imaginary parts: 2^2=4 and (7*i)^2=49*i^2

5. Substitute i^2=−1 into the expression: $4 - 49(-1)$.

6. Simplify the signs and add the numbers: $4 + 49 = 53$.

Final Answer

(2+7*i)*(2−7*i)=53

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