Algebra II : Basic Operations with Complex Numbers
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Example Questions
Example Question #71 : Basic Operations With Complex Numbers
Simplify:
Simplify each term. Recall that 
Simplify the expression.
The answer is:
Example Question #72 : Basic Operations With Complex Numbers
Solve:
Rewrite the terms with the actual value of the imaginary term.
Recall that 
This means that:
Replace this for all the terms.
The answer is:
Example Question #73 : Basic Operations With Complex Numbers
Evaluate:
Write the first few values of the imaginary term 
Rewrite the expression using the product of exponents.
The value of one to this power will remain the same.
The answer is:
Example Question #74 : Basic Operations With Complex Numbers
Compute:
To be able to evaluate the expression, we will need to write out the value of the imaginary terms.
Recall that:
Replace the terms.
The answer is:
Example Question #75 : Basic Operations With Complex Numbers
Evaluate:
Rewrite the problem as separate groups of binomials.
Use the FOIL method to expand the first two terms.
Simplify the right side.
Recall that since 
Multiply this value with the third binomial.
Simplify the terms.
The answer is:
Example Question #76 : Basic Operations With Complex Numbers
Solve:
In order to solve this expression, we will need to evaluate each term.
Use the property of exponents to subtract the powers in the fraction.
This term can be written as a fraction.
Recall that the imaginary term 
Replace the terms.
Solve the expression by replacing the values in the original expression.
The answer is:
Example Question #2091 : Mathematical Relationships And Basic Graphs
Simplify:
Write the first few powers of the imaginary term.
We can then rewrite the higher powered imaginary terms by the product of exponents.
Simplify the terms.
The answer is:
Example Question #78 : Basic Operations With Complex Numbers
Compute:
Identify the first two powers of the imaginary term.
Rewrite the expression as a product of exponents.
Negative one to an odd power will be negative one.
The answer is:
Example Question #79 : Basic Operations With Complex Numbers
Evaluate:
Write the first few powers of the imaginary term.
Change the higher ordered power by using the power rule of exponents.
A negative one to an odd power will be negative one.
The answer is:
Example Question #80 : Basic Operations With Complex Numbers
Add 
The complex conjugate of a complex number 
Therefore, the complex conjugate of 
Collect real parts and imaginary parts:
The imaginary parts cancel out:
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