Problem

\[ (7-5 i)(7+5 i) \] A. 14 B. 24 C. 74 D. $49-25 i$ E. $49-70 i-25 i^{2}$

Solution

Step 1 :Multiply the two complex numbers using the distributive property (FOIL method): \((7-5i)(7+5i) = 7(7) + 7(5i) - 5i(7) - 5i(5i)\)

Step 2 :Simplify the result: \(49 + 35i - 35i - 25i^2 = 49 - 25(-1)\)

Step 3 :Combine the real parts: \(49 + 25 = 74\)

Step 4 :\(\boxed{74}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8928/

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