Find the fourth roots of -17i?

amevaa0y

amevaa0y

Answered question

2022-01-30

Find the fourth roots of 17i?

Answer & Explanation

chukizosv

chukizosv

Beginner2022-01-31Added 8 answers

Step 1 Let us wrote 17i in polar form and as its modulus is 17 and number is 117×(i), we can write it as 17i=17e3π2i Let x=17i4, then x4=17i=17e3π2i Hence x=174e3π8i Other roots can be obtained by adding π2 to 3π8 in succession (as they are one-fourth of 2π) i.e. 174e7π8i, 174e11π8i and 174e15π8i To find them in the form of a+bi, you can use the following reiθ=rcosθ+isinθ

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