What is (3/4-(3i)/4)^{-4} ?

The solution to (3/4-(3i)/4)^{-4} is -64/81

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simplify (3/4-(3i)/4)^{-4}

simplify

(\frac{3}{4} - \frac{3 i}{4})^{- 4}

- \frac{64}{81}

Decimal Notation

- 0.79012 \dots

Solution steps

(\frac{3}{4} - \frac{3 i}{4})^{- 4}

Apply exponent rule:

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

(\frac{3}{4} - \frac{3 i}{4})^{- 4} = \frac{1}{( \frac{3}{4} - \frac{3 i}{4} ) ^{4}}

= \frac{1}{( \frac{3}{4} - \frac{3 i}{4} ) ^{4}}

Combine the fractions

\frac{3}{4} - \frac{3 i}{4} : \frac{3 - 3 i}{4}

= \frac{1}{( \frac{3 - 3 i}{4} ) ^{4}}

(\frac{3 - 3 i}{4})^{4} = \frac{( 3 - 3 i ) ^{4}}{4 ^{4}}

= \frac{1}{\frac{( 3 - 3 i ) ^{4}}{4 ^{4}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{4 ^{4}}{( 3 - 3 i ) ^{4}}

4^{4} = 256

= \frac{256}{( 3 - 3 i ) ^{4}}

Expand

(3 - 3 i)^{4} : - 324

= \frac{256}{- 324}

Factor the number:

256 = 4 \cdot 64

= \frac{4 \cdot 64}{- 324}

Factor the number:

324 = 4 \cdot 81

= \frac{4 \cdot 64}{- 4 \cdot 81}

Cancel the common factor:

4

= \frac{64}{- 81}

Apply the fraction rule:

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

= - \frac{64}{81}

2 x^{2} + 5 x - 1 > 0

x^{4} x^{5}

\frac{( x - 3 ) ( 4 - 2 x ) ( 1 - 3 x )}{( 1 - 4 x ) ( 5 - 3 x )} \leq 0

x^{4} - 8 x^{2} - 9

14 x \geq 56