What is (2-3i)^{-5} ?

The solution to (2-3i)^{-5} is (122)/(14884+597^2)-(597)/(14884+597^2)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2-3i)^{-5}

simplify

(2 - 3 i)^{- 5}

\frac{122}{14884 + 59 7 ^{2}} - \frac{597}{14884 + 59 7 ^{2}} i

Solution steps

(2 - 3 i)^{- 5}

Apply exponent rule:

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

(2 - 3 i)^{- 5} = \frac{1}{( 2 - 3 i ) ^{5}}

= \frac{1}{( 2 - 3 i ) ^{5}}

Expand

(2 - 3 i)^{5} : 597 i + 122

= \frac{1}{597 i + 122}

Rewrite

597 i + 122

in standard complex form:

122 + 597 i

= \frac{1}{122 + 597 i}

Multiply by the conjugate

\frac{122 - 597 i}{122 - 597 i}

= \frac{1 \cdot ( 122 - 597 i )}{( 122 + 597 i ) ( 122 - 597 i )}

Simplify

\frac{1 \cdot ( 122 - 597 i )}{( 122 + 597 i ) ( 122 - 597 i )} : \frac{122 - 597 i}{14884 + 59 7 ^{2}}

= \frac{122 - 597 i}{14884 + 59 7 ^{2}}

Rewrite in standard complex form:

\frac{122}{14884 + 59 7 ^{2}} - \frac{597}{14884 + 59 7 ^{2}} i

= \frac{122}{14884 + 59 7 ^{2}} - \frac{597}{14884 + 59 7 ^{2}} i

2 + (- 7)

\frac{x ^{2} - 25}{x ^{2} - 10 x + 25}

lo g_{4} (1 6^{2})

lo g_{3} (e) \cdot ln (\frac{1}{27})

What is (2-3i)^{-5} ?
The solution to (2-3i)^{-5} is (122)/(14884+597^2)-(597)/(14884+597^2)i