### All Algebra II Resources

## Example Questions

### Example Question #1 : Graphing Functions With Complex Numbers

Solve for

**Possible Answers:**

**Correct answer:**

Use the change of base formula for logarithmic functions and incorporate the fact that and

Or

can be solved using

### Example Question #2 : Graphing Functions With Complex Numbers

Where would fall on the number line?

**Possible Answers:**

to the left of

Cannot be determined

at

to the right of

**Correct answer:**

Cannot be determined

Imaginary numbers do not fall on the number line-- they are by definition not real numbers.

** If the question asked where falls on the number line, the answer would be to the left of 0, because .

### Example Question #3 : Graphing Functions With Complex Numbers

Write the complex number in polar form, that is, in terms of a distance from the origin on the complex plane and an angle from the positive -axis, , measured in radians.

**Possible Answers:**

**Correct answer:**

To see what the polar form of the number is, it helps to draw it on a graph, where the horizontal axis is the imaginary part and the vertical axis the real part. This is called the complex plane.

To find the angle , we can find its supplementary angle and subtract it from radians, so .

Using trigonometric ratios, and .

Then .

To find the distance , we need to find the distance from the origin to the point . Using the Pythagorean Theorem to find the hypotenuse , or .

### All Algebra II Resources

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