Algebra II : Basic Operations with Complex Numbers
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Example Questions
Example Question #21 : Basic Operations With Complex Numbers
Simplify:
Use FOIL to multiply the binomials:
Change 
Combine like terms:
Example Question #22 : Basic Operations With Complex Numbers
Find
This pattern repeats every four powers. Divide the power by 4:
Since the remainder is 3, it is equivalent to 
Example Question #81 : Imaginary Numbers
Simplify the following:
To solve this type of problem, it is easiest to divide the exponent by 4 and see what the remainder is. The reason we choose 4 is because 
So,
Example Question #21 : Basic Operations With Complex Numbers
Simplify the following expression:
To simplify the given expression, we can FOIL the two binomials, to get
which can be simplified to
given that 
Example Question #21 : Number Theory
Simplify:
First remember the form of the complex number:
Where "a" is the "Real" part, and "b" is the imaginary part.
Only the real parts can be combined together, and only the imaginary parts can be combined together.
Therefore the equation becomes after distributing the negative sign:
Collect the real and imaginary terms together:
Giving the answer:
Example Question #83 : Imaginary Numbers
Simplify:
To simplify the expression, we must keep in mind the following:
Now, we can use FOIL to simplify the product of the two binomials:
Next, simplify and combine like terms:
Example Question #22 : Basic Operations With Complex Numbers
Multiply:
To multiply this expression, use the distributive property:
Recall that
so
Therefore, your answer is
Example Question #27 : Basic Operations With Complex Numbers
Simplify:
To simplify, we can start by remembering the following:
Now, rewrite the first term with the above in mind:
Finally, FOIL the complex numbers:
Example Question #28 : Basic Operations With Complex Numbers
Simplify:
Multiply the conjugate of the denominator.
Solve the numerator. Remember that 
Solve the denominator. Simplify the terms with the 
Multiply these two terms together.
Divide the numerator with the denominator.
The answer is:
Example Question #29 : Basic Operations With Complex Numbers
Simplify:
In order to simplify this expression, pull out a common factor of 
Recall that since 
Replace that term in numerator.
The expression becomes:
This expression is equal to 
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