Question

How do you find the square root of a negative number? Explain the process

Answer 1

Answer:

A. $\sqrt{-64}$ = 8i

B. 8i + 5i = 13i

C.  8i - 5i = 3i

D. 8i x 5i = -40

Step-by-step explanation:

A. The square root of any negative number would lead to a complex number. Complex numbers are number which consist a complex part denoted by i.

-1 = $i^{2}$

$\sqrt{-1}$ = $\sqrt{i^{2} }$ = i

Example: 1. What is the square root of -64?

square root of -64 = $\sqrt{-64}$

                         = $\sqrt{-1 *64}$

                         = $\sqrt{-1}$ x $\sqrt{64}$

                         = i x 8

                         = 8i

$\sqrt{-64}$ = 8i

2. find the square root of -25.

$\sqrt{-25}$ = $\sqrt{-1*25}$

          = 5i

B. To add two complex numbers, they are considered as algebraic expressions.

Example, the sum of 8i and 5i can be determined as;

                 8i + 5i = 13i

C. To add two complex numbers, they are considered as algebraic expressions.

Example, the subtraction of 8i and 5i can be determined as;

                 8i - 5i = 3i

D. To multiply two complex numbers, the complex part is considered.

Example, determine the product of 8i and 5i.

8i x 5i = 8 x 5 x i x i

          = 40$i^{2}$

         = -40                (∵      $i^{2}$ = -1)

8i x 5i = -40