Solve x^{2}+i^8-i^6+i^4-i^2=0

$$x ^ { 2 } + i ^ { 8 } - i ^ { 6 } + i ^ { 4 } - i ^ { 2 } = 0$$

Solve for x

$$x=-2i$$

$$x=2i$$

Steps by Finding Square Root

Calculate i to the power of 8 and get 1.

$$x^{2}+1-i^{6}+i^{4}-i^{2}=0$$

Calculate i to the power of 6 and get -1.

$$x^{2}+1-\left(-1\right)+i^{4}-i^{2}=0$$

The opposite of -1 is 1.

$$x^{2}+1+1+i^{4}-i^{2}=0$$

Combine 1 and 1 to get 2\times 1.

$$x^{2}+2\times 1+i^{4}-i^{2}=0$$

Multiply 2 and 1 to get 2.

$$x^{2}+2+i^{4}-i^{2}=0$$

Calculate i to the power of 4 and get 1.

$$x^{2}+2+1-i^{2}=0$$

Add 2 and 1 to get 3.

$$x^{2}+3-i^{2}=0$$

Calculate i to the power of 2 and get -1.

$$x^{2}+3-\left(-1\right)=0$$

The opposite of -1 is 1.

$$x^{2}+3+1=0$$

Add 3 and 1 to get 4.

$$x^{2}+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-4$$

The equation is now solved.

$$x=2i x=-2i$$

Steps Using the Quadratic Formula

Calculate i to the power of 8 and get 1.

$$x^{2}+1-i^{6}+i^{4}-i^{2}=0$$

Calculate i to the power of 6 and get -1.

$$x^{2}+1-\left(-1\right)+i^{4}-i^{2}=0$$

The opposite of -1 is 1.

$$x^{2}+1+1+i^{4}-i^{2}=0$$

Combine 1 and 1 to get 2\times 1.

$$x^{2}+2\times 1+i^{4}-i^{2}=0$$

Multiply 2 and 1 to get 2.

$$x^{2}+2+i^{4}-i^{2}=0$$

Calculate i to the power of 4 and get 1.

$$x^{2}+2+1-i^{2}=0$$

Add 2 and 1 to get 3.

$$x^{2}+3-i^{2}=0$$

Calculate i to the power of 2 and get -1.

$$x^{2}+3-\left(-1\right)=0$$

The opposite of -1 is 1.

$$x^{2}+3+1=0$$

Add 3 and 1 to get 4.

$$x^{2}+4=0$$

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

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

Square 0.

$$x=\frac{0±\sqrt{-4\times 4}}{2}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16}}{2}$$

Take the square root of -16.

$$x=\frac{0±4i}{2}$$

Now solve the equation x=\frac{0±4i}{2} when ± is plus.

$$x=2i$$

Now solve the equation x=\frac{0±4i}{2} when ± is minus.

$$x=-2i$$

The equation is now solved.

$$x=2i x=-2i$$