# Trigonometry

1. Find the absolute value of the following complex number:

2. Choose the rectangular coordinates for the following polar coordinate:

3. Determine the rectangular form of the complex number:

4. Find the polar form of the following complex number:

5. When plotted on the rectangular coordinate system in which quadrant would the following point be located for this polar coordinate?

6. Find the power of the following complex number:

7. Find the value of the given complex number:

8. Choose the polar coordinates for the following rectangular coordinate

9. The following polar coordinates are multiple representations of the same point, True or False?

10. Find the polar form of the following expression:

11. Write each complex number in rectangular form. If necessary round to the nearest tenth.

12. Use DeMoirvre's Theorem to find the indicated power of the complex number. Write answer in rectangular form.

(Please see the attachment)

#### Solution Preview

The solution file is attached.

1. Find the absolute value of the following complex number:

a. z = 2 + 5i

|z| = √(2^2 + 5^2) = √29

2. Choose the rectangular coordinates for the following polar coordinate:

a. (6, )

x = r cos θ = 6 cos (3 π/2) = 0 and r sin θ = 6 sin (3 π/2) = -6

The rectangular coordinates are (x, y) = (0, -6)

3. Determine the rectangular form of the complex number:

z = 8 (cos = i sin )

cos π/2 = 0 and sin π/2 = 1

The rectangular form is z = 8[0 + ι(1)] = 8ι

4. Find the polar form of the following complex number:

a. z = 7 ( cos i sin )

The given complex number is already in the polar form.

5. When plotted on the ...

#### Solution Summary

The expert examines trigonometry absolute values for complex numbers. A complete, neat and step-by-step solutions are provided in the attached file.