High School Math : Imaginary Numbers

Example Questions

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Example Question #1 : Understanding Imaginary And Complex Numbers

No solution

Explanation:

First, factor the term in the radical.

Now, we can simplify.

Multiply:

Explanation:

FOIL:

Example Question #3 : Understanding Imaginary And Complex Numbers

Multiply:

Explanation:

Since  and  are conmplex conjugates, they can be multiplied according to the following pattern:

Example Question #4 : Understanding Imaginary And Complex Numbers

Multiply:

Explanation:

Since  and  are conmplex conjugates, they can be multiplied according to the following pattern:

Example Question #5 : Understanding Imaginary And Complex Numbers

Evaluate:

Explanation:

can be evaluated by dividing  by 4 and noting the remainder. Since  - that is, since dividing 45 by 4 yields remainder 1:

Evaluate:

Explanation:

Example Question #1 : Understanding Imaginary And Complex Numbers

What is the absolute value of

Explanation:

The absolute value is a measure of the distance of a point from the origin.  Using the pythagorean distance formula to calculate this distance.

Example Question #2 : Imaginary Numbers

Which of the following is equivalent to:

Explanation:

Recall that

Then, we have that .

Note that we used the power rule of exponents and the order of operations to simplify the exponent before multiplying by the coefficient.

Example Question #1 : Basic Operations With Complex Numbers

Simplify the expression.

None of the other answer choices are correct.

Explanation:

Combine like terms. Treat as if it were any other variable.

Substitute to eliminate .

Simplify.

Example Question #3 : Imaginary Numbers

Which of the following is equivalent to  ?

None of the other answer choices are correct.