What is (i^5+3)/(i^3-1) ?

The solution to (i^5+3)/(i^3-1) is -2+i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (i^5+3)/(i^3-1)

simplify

\frac{i ^{5} + 3}{i ^{3} - 1}

- 2 + i

Solution steps

\frac{i ^{5} + 3}{i ^{3} - 1}

Simplify

i^{5} : i

= \frac{i + 3}{i ^{3} - 1}

Simplify

i^{3} : - i

= \frac{i + 3}{- i - 1}

Rewrite

i + 3

in standard complex form:

3 + i

Rewrite

- i - 1

in standard complex form:

- 1 - i

= \frac{3 + i}{- 1 - i}

Multiply by the conjugate

\frac{- 1 + i}{- 1 + i}

= \frac{( 3 + i ) ( - 1 + i )}{( - 1 - i ) ( - 1 + i )}

Simplify

\frac{( 3 + i ) ( - 1 + i )}{( - 1 - i ) ( - 1 + i )} : \frac{- 4 + 2 i}{2}

= \frac{- 4 + 2 i}{2}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 4}{2} + \frac{2}{2} i

Simplify

\frac{- 4}{2} + \frac{2}{2} i : - 2 + i

= - 2 + i

x^{2} + x - 12

x^{4} - 256 \geq 0

\frac{1}{4} + 2

2 x^{2} + 8 x - 32

x^{2} - 4 = 0