Solve the following equation by identifying all of its roots including all real and complex numbers. In your final answer, include the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials.
x² + 1 = 0 x² = - 1 x 1 = i,  x 2 = - i x³ + 2 x = 0 x ( x² + 2 ) = 0 x 3 = 0 x² + 2 = 0 x² = - 2 x 4 = √2 i,  x 5 = - √2 i x² - 64 = 0 x² = 64 x 6 = - 8,  x 7 = 8 Answer: All roots are: { -√2 i,   -i,   i,  √2 i,  - 8,   0,  8 }
