Solve for z (complex solution)

z\in \mathrm{C}

$z∈C$

Solve for z

z\in \mathrm{R}

$z∈R$

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-9z-72=-9z-72

Use the distributive property to multiply -9 by z+8.

-9z-72+9z=-72

Add 9z to both sides.

-72=-72

Combine -9z and 9z to get 0.

\text{true}

Compare -72 and -72.

z\in \mathrm{C}

This is true for any z.

-9z-72=-9z-72

Use the distributive property to multiply -9 by z+8.

-9z-72+9z=-72

Add 9z to both sides.

-72=-72

Combine -9z and 9z to get 0.

\text{true}

Compare -72 and -72.

z\in \mathrm{R}

This is true for any z.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

Matrix

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \right]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $