A complex number is a number that consists of a real part and an imaginary part. It is written in the form a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit equal to the square root of -1.
To solve a complex number equation, first rewrite it in the form z = a + bi. Then, use the cubic formula z = ∛r(cosθ + isinθ), where r is the magnitude of z and θ is the angle between z and the positive real axis. Finally, substitute the values of r and θ into the formula to find the three possible solutions for z.
The cube root of -8 is -2, since (-2)^3 = -8.
A complex number equation can have up to three solutions, since a cubic equation has three roots. However, some solutions may be repeated or may not be real numbers.
No, complex numbers cannot be graphed on a number line since they have both real and imaginary components. They can be graphed on a complex plane, with the real part on the x-axis and the imaginary part on the y-axis.