Question

Use square roots to solve the equation x2 = −625 over the complex numbers. enter your answers in increasing order.

Answer 1

To solve for x in the equation x^2 = -625, we take the square root of 625, which is 25, and multiply it by the imaginary unit i to get the solutions: x = -25i and x = 25i.

Step-by-step explanation:

To solve the equation x2 = -625 over the complex numbers, we first look at the definition of a square root. The square root of a number is that number which, when multiplied by itself, gives the original number. In this case, since we have a negative number, we need to use the imaginary unit i where i2 = -1. So to get the square roots of -625, we first find the square root of 625, which is 25, and then multiply by i to account for the negative sign under the radical.

Therefore, the two complex solutions will be:

• x = 25i
• x = -25i

We list these in increasing order: -25i, 25i.