How do you find the fourth root of -8+8\sqrt{3}i?

absolutestylehc

absolutestylehc

Answered question

2022-01-31

How do you find the fourth root of 8+83i?

Answer & Explanation

votaren10

votaren10

Beginner2022-02-01Added 11 answers

8+83i has four fourth roots. These are 3+i,13i,3iand 1+3i.
Explanation:
Plot 8+83i on the complex plane and note that it has an argument of 120 and a modulus of (8)2+(83)2=16.
Consequently the argument and modulus of one root are 1204and 1614, that is, 30 and 2, which is 3+i. The other three have the same modulus and arguments which are multiples of 90 added on.

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