WRITING COMPLEX NUMBERS IN POLAR FORM WORKSHEET

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Plot the following points on a plane and evaluate their polar forms :

Problem 1 :

z = -1 + 2i

Solution

Write the complex number in polar form.

Problem 2 :

z = -3 - 3i

Solution

Problem 3 :

z = 3 - 4i

Solution

Problem 4 :

z = 2i

Solution

Problem 5 :

z = 3

Solution

Problem 6 :

z = -4

Solution

Problem 7 :

z = -5i

Solution

Answer Key

1)  āˆš5(cos (Ļ€ - tan-1(2)) + i sin (Ļ€ - tan-1(2)))

2)  3√2(cos (-3Ļ€/4) + i sin (-3Ļ€/4))

3)  5(cos (-tan-1(4/3)) + i sin (-tan-1(4/3)))

4)  2(cos (Ļ€/2) + i sin (Ļ€/2))

5)  3(cos 0 + i sin 0)

6)  4(cos Ļ€ + i sin Ļ€)

7)  4(cos (-Ļ€/2) + i sin (-Ļ€/2))

Plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians.

Problem 1 :

2 + 2i

Solution

Problem 2 :

1 + i√3

Solution

Problem 3 :

-1 - i

Solution

Problem 4 :

2 - 2i

Solution

Problem 5 :

-4i

Solution

Problem 6 :

-3i

Solution

Problem 7 :

2√3 - 2i

Solution

Problem 8 :

-2 + 2i√3

Solution

Problem 9 :

-3

Solution

Problem 10 :

-4

Solution

Problem 11 :

3√2 - 3i√2

Solution

Problem 12 :

-3 + 4i

Solution

Problem 13 :

-2 + 3i

Solution

Problem 14 :

2 - i√3

Solution

Problem 15 :

1 - i√5

Solution

Answer Key

1)  2 + 2i = 2√2(cos Ļ€/4 + i sin Ļ€/4)

2)  1 + i√3 = 2(cos Ļ€/3 + i sin Ļ€/3)

3)  

-1-i=2cos -3šœ‹4+i sin -3šœ‹4

4) 

2-2i=22cos -šœ‹4+i sin -šœ‹4

5)  

0-4i=4cos -šœ‹2+i sin -šœ‹2

6)  

0-3i=3cos -šœ‹2+i sin -šœ‹2

7)

23-2i=4cos -šœ‹6+i sin -šœ‹6

8)

-2+2i3=4cos -šœ‹3+i sin -šœ‹3

9)  -3 + 0i = 3(cos Ļ€ + i sin Ļ€)

10)  -4 + 0i = 4(cos Ļ€ + i sin Ļ€)

11)  

32-32i=6cos -šœ‹4+i sin -šœ‹4

12)

-3+4i=5cos šœ‹-tan-143+i sin šœ‹-tan-143

13)

-2+3i=13cos šœ‹-tan-132+i sin šœ‹-tan-132

14)

2-3i=7cos -tan-132+i sin -tan-132

15)

1-5i=6cos -tan-15+i sin -tan-15

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