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Complex Numbers

Problems

Polar Form of Complex Numbers

How to Cite This SparkNote

Problem : Convert the complex number 1 + ı to polar form.

1 + ı = 2[cos() + ısin()] .

Problem : Convert the complex number [cos() + ısin()] to standard form.

[cos() + ısin()] = 0 + 2ı .

Problem : What is 3[cos() + ısin()] divided by 2[cos() + ısin()] ? Write the answer in standard form.

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Problem : What is ( + ı)7 ?

(2 + 2ı)7 = (2[cos() + ısin()])7
= 27[cos() + ısin()]
= 128[ - ı]
= 64 -64ı .

Problem : What are the 4 th roots of 3 ?

3 = 3[cos(0) + ısin(0)] . The four roots r 1, r 2, r 3 , and r 4 are given by [cos() + ısin()] , where k = 0, 1, 2, 3 .

r 1 = [cos(0) + ısin(0)
= [1 + 0ı]
= .

r 2 = [cos() + ısin()]
= [0 + 1ı] = ı .

r 3 = [cos(Π) + ısin(Π)]
= [- 1 + 0ı]
= - .

r 4 = [cos() + ısin()] = [0 - 1ı]
= - ı .

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