Find the square root of a complex number.

wabennestvzz

wabennestvzz

Answered question

2023-02-06

Find the square root of a complex number.

Answer & Explanation

Marcel Yoder

Marcel Yoder

Beginner2023-02-07Added 4 answers

We convert into trigonometric form
z = r [ cos ( θ ) + i sin ( θ ) ]
z n = r n [ cos ( n θ ) + i sin ( n θ ) ] , n = 1 2 (in our case)
I would write n z = z 1 n = r 1 n [ cos ( θ + 2 k π n ) + i sin ( θ + 2 k π n ) ] , k = 0 . . n - 1 to calculate a complex number's nth root.

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