Question

write the equivalent expression for $(-2 + 4i)^2$ in $a + bi$ form
a $12 + 16i$
b $-12 + 16i$
c $-12 - 16i$
d $12 - 16i$

Explanation:

Step1: Expand using square formula

$$(-2 + 4i)^2 = (-2)^2 + 2(-2)(4i) + (4i)^2$$

Step2: Calculate each term

$$(-2)^2 = 4,\ 2(-2)(4i) = -16i,\ (4i)^2 = 16i^2$$

Step3: Substitute $i^2=-1$

$$16i^2 = 16(-1) = -16$$

Step4: Combine all terms

$$4 - 16i - 16 = (4-16) -16i = -12 -16i$$

Answer:

C. $-12 -16i$