WRITING COMPLEX NUMBERS IN POLAR FORM WORKSHEET
Plot the following points on a plane and evaluate their polar forms :
Problem 1 :
z = -1 + 2i
Write the complex number in polar form.
Problem 2 :
z = -3 - 3i
Problem 3 :
z = 3 - 4i
Problem 4 :
z = 2i
Problem 5 :
z = 3
Problem 6 :
z = -4
Problem 7 :
z = -5i
Answer Key
1) √5(cos (π - tan-1(2)) + i sin (π - tan-1(2)))
2) 3√2(cos (-3π/4) + i sin (-3π/4))
3) 5(cos (-tan-1(4/3)) + i sin (-tan-1(4/3)))
4) 2(cos (π/2) + i sin (π/2))
5) 3(cos 0 + i sin 0)
6) 4(cos π + i sin π)
7) 4(cos (-π/2) + i sin (-π/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
Problem 2 :
1 + i√3
Problem 3 :
-1 - i
Problem 4 :
2 - 2i
Problem 5 :
-4i
Problem 6 :
-3i
Problem 7 :
2√3 - 2i
Problem 8 :
-2 + 2i√3
Problem 9 :
-3
Problem 10 :
-4
Problem 11 :
3√2 - 3i√2
Problem 12 :
-3 + 4i
Problem 13 :
-2 + 3i
Problem 14 :
2 - i√3
Problem 15 :
1 - i√5
Answer Key
1) 2 + 2i = 2√2(cos π/4 + i sin π/4)
2) 1 + i√3 = 2(cos π/3 + i sin π/3)
3)
4)
5)
6)
7)
8)
9) -3 + 0i = 3(cos π + i sin π)
10) -4 + 0i = 4(cos π + i sin π)
11)
12)
13)
14)
15)
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