# College Algebra : Complex Numbers

## Example Questions

### Example Question #401 : College Algebra

Simplify the following:

Explanation:

To solve, you must remember the basic rules for i exponents.

Given the prior, simply plug into the given expression and combine like terms.

### Example Question #12 : Complex Numbers

Given the following quadratic, which values of  will produce a set of complex valued solutions for

2 and 3

1, 3 and 5

None of these, all produce real-valued solutions for

1 and 3

1, 4, and 5

1, 3 and 5

Explanation:

In order to determine if a quadratic equation  will have real-valued or complex-valued solutions compute the discriminate:

If the discriminate is negative, we will have complex-valued solutions. If the discriminate is positive, we will have real-valued solutions.

This arises from the fact that the quadratic equation has the square-root term,

Evaluate the discriminate for

-79<0 so the quadratic has complex roots for

Evaluate the discriminate for

The discriminate is positive, therefor the quadratic has real roots for

### Example Question #121 : Review And Other Topics

Evaluate:

Explanation:

Recall that , and .

Each imaginary term can then be factored by using .

Replace the numerical values for each term.

### Example Question #14 : Complex Numbers

Simplify:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the negative:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 2+4i

### Example Question #15 : Complex Numbers

Simplify:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 10-4i

### Example Question #16 : Complex Numbers

Simplify:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 10+2i

### Example Question #17 : Complex Numbers

Simplify:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 7+18i

### Example Question #18 : Complex Numbers

Simplify:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 9+2i

### Example Question #19 : Complex Numbers

Simplify:

Explanation:

When simplifying expressions with complex numbers, use the same techniques and procedures as normal.

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of -1+9i

Simplify: