Question

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

02

and provide two examples.

In your own words, explain the process for adding and subtracting complex

1-

numbers.

= In your own words, explain the process of multiplying complex numbers.

Answer 1

A.
`√(-64)` = 8i

B. 8i + 5i = 13i

C. 8i - 5i = 3i

D. 8i x 5i = -40

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)`

`√(-1)` =
`\sqrt{i^(2) }` = i

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

square root of -64 =
`√(-64)`

=
`√(-1 *64)`

=
`√(-1)` x
`√(64)`

= i x 8

= 8i

`√(-64)` = 8i

2. find the square root of -25.

`√(-25)` =
`√(-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