Find each of the products and match each expression with the corresponding answer.
-$60 + 32 i$
A) $( 8 + 2 i ) ^ { 2 }$
B) $( 8 - 2 i ) ^ { 2 }$

Question

Find each of the products and match each expression with the corresponding answer.
-$60 + 32 i$ 
A) $( 8 + 2 i ) ^ { 2 }$ 
B) $( 8 - 2 i ) ^ { 2 }$

Quizplus · Accepted Answer

Using FOIL, we get:

$$(8 + 2i)^2 = (8+2i)(8+2i)$$
$$= 8 \cdot 8 + 8 \cdot 2i + 2i \cdot 8 + 2i \cdot 2i$$
$$= 64 + 32i + 16i^2$$
Since $i^2 = -1$, we can simplify to:
$$= 64 + 32i - 16$$
$$= 48 + 32i$$

which matches with $60 + 32i$.

On the other hand,

$$(8-2i)^2 = (8-2i)(8-2i)$$
$$= 8 \cdot 8 + 8 \cdot (-2i) - 2i \cdot 8 + (-2i) \cdot (-2i)$$
$$= 64 - 32i - 16$$
$$= 48 - 32i$$

which does not match with $60 + 32i$.

Find Each of the Products and Match Each Expression with the Corresponding