# Precalculus : Polar Coordinates and Complex Numbers

## Example Questions

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

Determine the length of

Explanation:

, so

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

Solve for all possible solutions to the quadratic expression:

Explanation:

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:

Explanation:

Solve for complex values of  using the quadratic formula:

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

Determine the length of .

Explanation:

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).

Explanation:

To solve for the roots, just set equal to zero and solve for z using the quadratic formula, which is

and now setting both  and  equal to zero we end up with the answers  and  and so the correct answer is .

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

Solve for all possible solutions to the quadratic expression:

Explanation:

Solve for complex values of  using the quadratic formula: .

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

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

Explanation:

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:

Explanation:

Distribute the coefficient 2, and evaluate each term:

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

Convert the following to rectangular form:

Explanation:

Distribute the coefficient and simplify:

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

Represent the polar equation:

in rectangular form.