Solve z^2+3=0

$$z ^ { 2 } + 3 = 0$$

Solve for z

$$z=-\sqrt{3}i\approx -0-1.732050808i$$

$$z=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$z^{2}=-3$$

The equation is now solved.

$$z=\sqrt{3}i z=-\sqrt{3}i$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$z^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 3}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 3}}{2}$$

Multiply -4 times 3.

$$z=\frac{0±\sqrt{-12}}{2}$$

Take the square root of -12.

$$z=\frac{0±2\sqrt{3}i}{2}$$

Now solve the equation z=\frac{0±2\sqrt{3}i}{2} when ± is plus.

$$z=\sqrt{3}i$$

Now solve the equation z=\frac{0±2\sqrt{3}i}{2} when ± is minus.

$$z=-\sqrt{3}i$$

The equation is now solved.

$$z=\sqrt{3}i z=-\sqrt{3}i$$