What is (i^{1069}-2)^{-1} ?

The solution to (i^{1069}-2)^{-1} is -2/5-1/5 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (i^{1069}-2)^{-1}

simplify

(i^{1069} - 2)^{- 1}

- \frac{2}{5} - \frac{1}{5} i

Solution steps

(i^{1069} - 2)^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(i^{1069} - 2)^{- 1} = \frac{1}{i ^{1069} - 2}

= \frac{1}{i ^{1069} - 2}

Simplify

i^{1069} : i

= \frac{1}{i - 2}

Rewrite

i - 2

in standard complex form:

- 2 + i

= \frac{1}{- 2 + i}

Multiply by the conjugate

\frac{- 2 - i}{- 2 - i}

= \frac{1 \cdot ( - 2 - i )}{( - 2 + i ) ( - 2 - i )}

Simplify

\frac{1 \cdot ( - 2 - i )}{( - 2 + i ) ( - 2 - i )} : \frac{- 2 - i}{5}

= \frac{- 2 - i}{5}

Apply the fraction rule:

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

= \frac{- 2}{5} + \frac{- 1}{5} i

Simplify

\frac{- 2}{5} + \frac{- 1}{5} i : - \frac{2}{5} - \frac{1}{5} i

= - \frac{2}{5} - \frac{1}{5} i

2 (n + 2 n - 5)

a^{2} - 22 a + 121

\frac{7 - ( - 3 )}{4}

40 x^{3} y^{2}