Question

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

x2+75=0



Enter your answers, as exact values, in the boxes.

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√(-75)=\pm√((-1)75)=\pm√(-1)√(75)=\pm√(75)i`

So, the two answers are

`√(75)i,\quad -√(75)i`

Answer 2

-5√3 i, 5√3 i.

Explanation:

x^2 + 75 = 0

x^2 = -75

x = +/- √-75

= +/- √75 i

= +/- 5√3 i.