Write each expression in standard form for complex numbers.

1. (-2 + 3i) - (1 - 2i)

2. (2 + i)2

3. 

   For the complex number -5 + i, name its

4. conjugate.

5. absolute value.

6. opposite.

7. Write the complex number 4(cos 30° + i sin 30°) in standard form.

8. Write the complex number 3 - 3i in trigonometric form.

    Find each product and quotient and leave your answers in trigonometric form.

9. 2(cos 35° + i sin 35°) · 3(cos 15° + i sin 15°)

10. 

11. Use DeMoivre's Theorem to find (1 + i)⁴ in standard form.

12. Find the two square roots of z = 2 + 2i in standard form.

13. Find the three cube roots of z = 8i in trigonometric form.

14. For the point (2, 135°), give three ordered pairs in polar coordinates (with r positive and -360°£ q £ 360°) that name the same point and then convert (2, 135°) to rectangular coordinates.

15. Convert (-3, 0) to polar coordinates with r positive and 0°£ q £ 360°.

16. Convert (-2, 2) to polar coordinates with r positive and 0°£ q £ 360°.

17. Write r = 4 sin q with rectangular coordinates.

18. Graph r = 2 + 2 sin q in polar coordinates.