Solve A^2=-1

$$A ^ { 2 } = - 1$$

Solve for A

$$A=-i$$

$$A=i$$

Steps by Finding Square Root

The equation is now solved.

$$A=i A=-i$$

Steps Using the Quadratic Formula

Add 1 to both sides.

$$A^{2}+1=0$$

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

$$A=\frac{0±\sqrt{0^{2}-4}}{2}$$

Square 0.

$$A=\frac{0±\sqrt{-4}}{2}$$

Take the square root of -4.

$$A=\frac{0±2i}{2}$$

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

$$A=i$$

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

$$A=-i$$

The equation is now solved.

$$A=i A=-i$$