Use square roots to solve the equation x2 = –64 over the complex numbers. Select any solutions that apply.
A. 8i
B. –8
C. –8i2
D. –8i

Answers

Answer 1

Answer:

Options A and D are correct

Step-by-step explanation:

Here, we want to find the square root of the negative number;

x^2 = -64

x^2 = 64 * -1

x= √64 * √-1

Mathematically we can write the √-1 as i

X = √64 * i

Square root of 64 is plus or minus 8

so x = -8i or 8i

Answer 2

The solutions of an equation are the true values of the equation.

The expression that represents the solution(s) of [tex]\mathbf{8i}[/tex] is [tex]\mathbf{-8i}[/tex]

The equation is given as:

[tex]\mathbf{x^2 = -64}[/tex]

Take square roots of both sides

[tex]\mathbf{x = \pm\sqrt{-64}}[/tex]

Expand

[tex]\mathbf{x = \pm(\sqrt{64} \times \sqrt{-1})}[/tex]

[tex]\mathbf{x = \pm(8 \times \sqrt{-1})}[/tex]

In complex numbers,

[tex]\mathbf{ \sqrt{-1} = i}[/tex]

So, we have:

[tex]\mathbf{x = \pm(8 \times i)}[/tex]

[tex]\mathbf{x = \pm8i}[/tex]

Split

[tex]\mathbf{x = 8i\ or -8i}[/tex]

So, the expression that represents the solution(s) of [tex]\mathbf{8i}[/tex] is [tex]\mathbf{-8i}[/tex]

Read more about expressions at:

https://brainly.com/question/23767452


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