What are the solutions to the equation x^5=i ?

The solutions to the equation x^5=i are

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^5=i

x^{5} = i

x = \frac{2 5 + 5}{4} + i \frac{2 3 - 5}{4}, x = i, x = - \frac{2 5 + 5}{4} + i \frac{2 3 - 5}{4}, x = - \frac{10 - 2 5}{4} + i \frac{- 1 - 5}{4}, x = \frac{10 - 2 5}{4} + i \frac{- 1 - 5}{4}

Solution steps

x^{5} = i

For

z^{n} = a

the solutions are

k = 0, 1, \dots, n - 1

For

n = 5, a = i

∣ a ∣ = 1

ar g (a) = \frac{π}{2}

Simplify

x = \frac{2 5 + 5}{4} + i \frac{2 3 - 5}{4}, x = i, x = - \frac{2 5 + 5}{4} + i \frac{2 3 - 5}{4}, x = - \frac{10 - 2 5}{4} + i \frac{- 1 - 5}{4}, x = \frac{10 - 2 5}{4} + i \frac{- 1 - 5}{4}

r^{5} + 5 r^{4} - 2 r^{3} - 10 r^{2} + r + 5 = 0

x^{3} - 3 x^{2} + 7 x - 5

\frac{1}{3} x^{3} + x^{2} + 1 = 0

(x - 1)^{2} (x - 2) = 0

20 x^{3} + 44 x^{2} - 17 x - 5 = 0

What are the solutions to the equation x^5=i ?
The solutions to the equation x^5=i are
Find the zeros of x^5=i
The zeros of x^5=i are