Algebra II : Imaginary Numbers
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Example Questions
Example Question #31 : 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 #38 : 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:
Example Question #41 : Basic Operations With Complex Numbers
Multiply:
Use the distributive property to multiply:
Recall that
so that you get
which gives you a final answer of
Example Question #42 : Basic Operations With Complex Numbers
Evaluate:
In order to solve this, we will need to convert the imaginary terms.
Recall that 
Replace the values with the imaginary terms.
The answer is:
Example Question #101 : Imaginary Numbers
Simplify:
The negative terms inside the square roots will be imaginary.
The term, 
Rewrite the terms using this as the common factor so that we can replace 
Replace the terms and simplify the square roots.
The answer is:
Example Question #102 : Imaginary Numbers
Solve:
Evaluate each imaginary term. The value of 
Evaluate 
Combine and subtract the two terms.
The answer is:
Example Question #2063 : Mathematical Relationships And Basic Graphs
This problem requires you to use FOIL to multiply the binomials.
Multiply the first terms
then the outside terms
next the inside terms
and finally the last terms
Put those together to get
Recall that
Therefore, your answer is
Example Question #2061 : Mathematical Relationships And Basic Graphs
Simplify:
Recall that 
Notice that this pattern will repeat.
Convert each term of 
Rewrite the expression.
The answer is:
Example Question #101 : Imaginary Numbers
Example Question #102 : Imaginary Numbers
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