Question

What are the solutions to the equation over the complex numbers?

Answer 1

Start with

$x^2+75=0$

Subtract 75 from both sides:

$x^2=-75$

Take the square root of both sides. As usual, this implies a double sign on the right hand side:

$x=\pm\sqrt{-75}=\pm\sqrt{(-1)75}=\pm\sqrt{-1}\sqrt{75}=\pm\sqrt{75}i$

So, the two answers are

$\sqrt{75}i,\quad -\sqrt{75}i$

Answer 2

Answer:

  -5√3 i,   5√3 i.

Step-by-step explanation:

x^2 + 75 = 0

x^2 = -75

x = +/- √-75

= +/- √75 i

=  +/- 5√3 i.