The expression "a + bi" represents a complex number in the form of a real number (a) plus an imaginary number (bi).
To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. To multiply complex numbers, use the FOIL method and remember that i2 = -1. To divide complex numbers, multiply the numerator and denominator by the complex conjugate, which is the same number with the sign of the imaginary part changed.
To convert a complex number in the form "a + bi" to polar form, use the formula r = √(a2 + b2) to find the distance from the origin to the point in the complex plane, and then use the formula θ = tan-1(b/a) to find the angle of the vector from the positive real axis.
To graph a complex number in the form "a + bi", plot the real part (a) on the horizontal axis and the imaginary part (b) on the vertical axis, just like plotting points on a Cartesian plane. The resulting point will represent the complex number's location in the complex plane.
Yes, a complex number in the form "a + bi" can have a negative imaginary part. The imaginary part represents the coefficient of the imaginary unit i, which can be positive, negative, or zero.