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

Answer

Expert–verified

Hide Steps

Answer

$\boxed{74}$

Steps

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 ：$\boxed{74}$