Algebra II : Basic Operations with Complex Numbers
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Example Questions
Example Question #31 : Basic Operations With Complex Numbers
Nothing can be simplified in either parentheses, so the first step is to distribute the negative sign to the second parentheses
Then, you combine similar terms remembering that terms with i cannot combine with those with no i
Example Question #31 : Basic Operations With Complex Numbers
Simplify:
In order to simplify this, we will need to identify the solution to each term with an imaginary power.
Recall that 
Rewrite and replace each term with the simplified forms.
Combine like-terms.
The answer is:
Example Question #33 : Basic Operations With Complex Numbers
This problem should be foiled. Multiply the first two numbers of each parentheses, the outer numbers of the parentheses, the inner numbers of the two parentheses, and the last numbers of the parentheses.
Combine like terms
Simplify the imaginary numbers. I squared equals -1
Example Question #34 : Basic Operations With Complex Numbers
First perform the multiplication on the coefficients and the i's
i cubed is equal to negative i
Example Question #35 : Basic Operations With Complex Numbers
Multiply the coefficients and the i's together
i to the fourth power is the same as the number one.
Example Question #36 : Basic Operations With Complex Numbers
This problem should be foiled. Multiply the first numbers of the parentheses, the outer numbers of the parentheses, the inner numbers of the parentheses, and the last numbers of the parentheses
Combine like terms
Simplify i squared to negative one
Example Question #37 : Basic Operations With Complex Numbers
This problem can either be solved by simplifying the numbers in the parentheses first or by distributing the 8i to all terms in the parentheses. I will show simplifying the parentheses first.
Remember that i squared can be simplified to negative one and like terms can be combined.
Now distribute the 8i to both terms of the parentheses.
Again, i squared can be changed to negative one
Example Question #38 : Basic Operations With Complex Numbers
Nothing can be simplified in the parentheses but the sign outside of each parentheses can be distributed to each number inside.
Combine like terms to get the answer
Example Question #39 : Basic Operations With Complex Numbers
This problem should be foiled. Multiply the first numbers, the outer numbers, the inner numbers, and the last numbers of the parentheses.
Combine like terms
Simplifying i squared to negative one
Example Question #40 : Basic Operations With Complex Numbers
Evaluate:
Recall that 
Write the first few terms of the powers of the imaginary number.
Notice that the pattern will repeat itself for higher powers.
Rewrite the expression given as a product of exponents.
Simplify using the known values of 
The quantity of a negative number to an odd power will result in a negative number.
The answer is:
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