College Algebra : Review and Other Topics
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Example Questions
Example Question #3 : Complex Numbers
The answer is not present.
Combine like terms:
Distribute:
Combine like terms:
Example Question #4 : Complex Numbers
Rationalize the complex fraction:
To rationalize a complex fraction, multiply numerator and denominator by the conjugate of the denominator.
Example Question #5 : Complex Numbers
Multiply:
Use FOIL to multiply the two binomials.
Recall that FOIL stands for Firsts, Outers, Inners, and Lasts.
Remember that
Example Question #121 : Review And Other Topics
Simplify the following:
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 #121 : Review And Other Topics
Given the following quadratic, which values of 
2 and 3
1 and 3
1, 4, and 5
None of these, all produce real-valued solutions for 
1, 3 and 5
1, 3 and 5
In order to determine if a quadratic equation 
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 #13 : Complex Numbers
Evaluate:
Recall that 
Each imaginary term can then be factored by using 
Replace the numerical values for each term.
The answer is:
Example Question #11 : Complex Numbers
Simplify:
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 #121 : Review And Other Topics
Simplify:
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 #121 : Review And Other Topics
Simplify:
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 #121 : Review And Other Topics
Simplify:
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
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