What is factor (2z+1)/(z^2-iz+6) ?

The solution to factor (2z+1)/(z^2-iz+6) is (6+z^2+12z+2z^3)/(36+z^4+13z^2)+i(z+2z^2)/(36+z^4+13z^2)

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factor (2z+1)/(z^2-iz+6)

factor

\frac{2 z + 1}{z ^{2} - i z + 6}

\frac{6 + z ^{2} + 12 z + 2 z ^{3}}{36 + z ^{4} + 13 z ^{2}} + i \frac{z + 2 z ^{2}}{36 + z ^{4} + 13 z ^{2}}

Solution steps

\frac{2 z + 1}{z ^{2} - i z + 6}

Rationalize

\frac{2 z + 1}{z ^{2} - i z + 6} : \frac{( 2 z + 1 ) ( z ^{2} + i z + 6 )}{z ^{4} + 13 z ^{2} + 36}

= \frac{( 2 z + 1 ) ( z ^{2} + i z + 6 )}{z ^{4} + 13 z ^{2} + 36}

Factor

z^{4} + 13 z^{2} + 36 : (z^{2} + 4) (z^{2} + 9)

= \frac{( 2 z + 1 ) ( z ^{2} + i z + 6 )}{( z ^{2} + 4 ) ( z ^{2} + 9 )}

Rewrite

\frac{( 2 z + 1 ) ( z ^{2} + 6 + i z )}{( z ^{2} + 4 ) ( z ^{2} + 9 )}

in standard complex form:

\frac{2 z ^{3} + 12 z + z ^{2} + 6}{z ^{4} + 13 z ^{2} + 36} + \frac{2 z ^{2} + z}{z ^{4} + 13 z ^{2} + 36} i

= \frac{2 z ^{3} + 12 z + z ^{2} + 6}{z ^{4} + 13 z ^{2} + 36} + \frac{2 z ^{2} + z}{z ^{4} + 13 z ^{2} + 36} i

(sec (+ tan (x)))^{2}

(x^{2}) + 43 x + 24

\frac{5}{4} + \frac{8}{6}

2 x y \frac{d y}{d x} + y^{2}

\frac{d}{d y} ((x) (cos (x y)))

What is factor (2z+1)/(z^2-iz+6) ?
The solution to factor (2z+1)/(z^2-iz+6) is (6+z^2+12z+2z^3)/(36+z^4+13z^2)+i(z+2z^2)/(36+z^4+13z^2)