Question

which of the following is equivalent to the expression $(2cdot5i)^{2}$? (1 point)
$5icdot2$
$100$
$100i$
$- 100$

Explanation:

Step1: Expand the square

Use the formula $(a\cdot b)^2=a^2\cdot b^2$. Here $a = 2$ and $b = 5i$, so $(2\cdot5i)^2=2^2\cdot(5i)^2$.
$2^2\cdot(5i)^2=4\cdot25i^2$.

Step2: Recall the value of $i^2$

We know that $i^2=- 1$.
$4\cdot25i^2=4\times25\times(-1)$.

Step3: Calculate the result

$4\times25\times(-1)=-100$.

Answer:

$-100$