### All Precalculus Resources

## Example Questions

### Example Question #7 : Find The Roots Of Complex Numbers

Determine the length of

**Possible Answers:**

**Correct answer:**

, so

### Example Question #8 : Find The Roots Of Complex Numbers

Solve for all possible solutions to the quadratic expression:

**Possible Answers:**

**Correct answer:**

Solve for complex values of m using the aforementioned quadratic formula:

### Example Question #9 : Find The Roots Of Complex Numbers

Which of the following lists all possible solutions to the quadratic expression:

**Possible Answers:**

**Correct answer:**

Solve for complex values of using the quadratic formula:

### Example Question #10 : Find The Roots Of Complex Numbers

Determine the length of .

**Possible Answers:**

**Correct answer:**

To begin, we must recall that . Plug this in to get . Length must be a positive value, so we'll take the absolute value: . Therefore the length is 3.

### Example Question #21 : Powers And Roots Of Complex Numbers

Solve for (there may be more than one solution).

**Possible Answers:**

### Example Question #11 : Find The Roots Of Complex Numbers

Solve for all possible solutions to the quadratic expression:

### Example Question #23 : Powers And Roots Of Complex Numbers

Solve for (there may be more than one solution).

**Possible Answers:**

**Correct answer:**

To solve for the roots, just set equal to zero and solve for using the quadratic formula (): and now setting both and equal to zero we end up with the answers and .

### Example Question #1 : Express Complex Numbers In Rectangular Form

Convert the following to rectangular form:

**Possible Answers:**

**Correct answer:**

Distribute the coefficient 2, and evaluate each term:

### Example Question #2 : Express Complex Numbers In Rectangular Form

Convert the following to rectangular form:

**Possible Answers:**

**Correct answer:**

Distribute the coefficient and simplify:

### Example Question #3 : Express Complex Numbers In Rectangular Form

Represent the polar equation:

in rectangular form.

**Possible Answers:**

**Correct answer:**

Using the general form of a polar equation:

we find that the value of is and the value of is .

The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

distributing the 3, we obtain the final answer of:

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