Perform the indicated operation and simplify. Write the result in the form a $a + bi$
-$( 2 + 4 \mathrm { i } ) ( 2 - 4 \mathrm { i } )$
A) $20 + 0 \mathrm { i }$
B) $4 - 16 i$
C) $- 12 + 0 \mathrm { i }$
D) $4 - 16 \mathrm { i } ^ { 2 }$

Question

Quizplus · Accepted Answer

Multiplying the complex numbers $(2 + 4i)$ and $(2 - 4i)$ using the distributive property (FOIL method), we get $2*2 + 2*(-4i) + 4i*2 + 4i*(-4i) = 4 - 8i + 8i - 16i^2$. Since $i^2 = -1$, the expression simplifies to $4 + 16 = 20$, or $20 + 0i$.

Perform the Indicated Operation and Simplify a+bia + bia+bi - (2+4i)(2−4i)( 2 + 4 \mathrm { i } ) ( 2 - 4 \mathrm { i } )(2+4i)(2−4i)

Perform the Indicated Operation and Simplify $a + bi$ - $( 2 + 4 \mathrm { i } ) ( 2 - 4 \mathrm { i } )$