Question

Use square roots to solve the equation x ^ 2 = - 25 over the complex numbers. Select any solutions that apply A.-5 B. -5i C. -5i^2 D.5i

Answer 1

$\begin{gathered}\\ \sf\longmapsto x^{2}=-25\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto x^{2}=±5i\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto x = - 5 i\\ x = 5i\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto x_{1} = - 5i \: , x_{2} = 5i\end{gathered}$

Answer 2

Answer:

B. $-5i$

D. $5i$

Step-by-step explanation:

Remember that the imaginary unit is equal to:

$i^2 = -1$

And getting the square root in both sides of the equation we get:

$i = \sqrt{-1} \quad \land \quad -i = \sqrt{-1}$

The with our expression we develop of the next way:

$x^2 = -25\\x = \sqrt{-25}$

However in the real numbers doesn't exist solution for such operation then you use the complex numbers for represent the operation.

$x = 5i \quad \land \quad x = -5i$

In this occasion we use $i$ and $-i$ because both represent a negative square root, so our final answer is:

B and D