Complex Numbers Polar And Rectangular Form Worksheet
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1
21. Write the complex numbers in polar form:
a. 1 + i
b.
1 + i
c. 1
3i
d. 4
4i
e.
2
2. Write the following complex number in rectangular form:
2π
2π
a. 2 cos
+ i sin
3
3
7π
7π
b. 4 cos
+ i sin
4
4
5π
5π
c. 2 cos
+ i sin
6
6
3π
3π
d. 3 cos
+ i sin
2
2
3. Simplify the expression and write your answer in standard form a + bi
2π
2π
a. 4 cos
+ i sin
9
9
π
π
b. 2 cos
+ i sin
10
10
5π
5π
c.
2 cos
+ i sin
16
16
3π
3π
d.
5 cos
+ i sin
16
16
5π
5π
e.
3 cos
+ i sin
18
18
f. (1
i)
g.
3
i
4. Find all cube roots of 1 + i.
5. Find all fourth roots of
3
i.
6. Find all fourth roots of 4
4 3i.
7. Find all the fifth roots of i
8. Find all the fourth roots of unity.
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