What is 1/((2-3i)^5) ?

The solution to 1/((2-3i)^5) is (122)/(14884+597^2)-(597)/(14884+597^2)i

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simplify 1/((2-3i)^5)

simplify

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

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

Solution steps

\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

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(3 x - y) (2 x - 5 y)

(x^{3} + x y^{2} + y) d y + (x^{2} y + y^{3} + x) d x

(1 - cot (x))^{2}

(2 x + 2)^{2}

What is 1/((2-3i)^5) ?
The solution to 1/((2-3i)^5) is (122)/(14884+597^2)-(597)/(14884+597^2)i