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COMPLEX NUMBER
COMPLEX NUMBER
For real numbers a and b, the number a + bi is a complex number. If a = 0 and b ≠ 0, the complex number bi is an imaginary number.
Because complex numbers are two-dimensional, they cannot be plotted on a one-dimensional number line, but they may be plotted on the complex plane. The complex plane is similar to the Cartesian plane in appearance, but the horizontal axis is the real axis and the vertical axis is the imaginary axis.
POLAR FORM OF A COMPLEX NUMBER
POLAR FORM OF A COMPLEX NUMBER
The polar, or trigonometric, form of the complex number z = a + bi is given by:
z = r(cos θ + isin θ)
where r is the modulus of z and θ is the argument of z.
Khan Academy Practice:
Khan Academy Practice:
DISTANCE AND MIDPOINT
DISTANCE AND MIDPOINT
If two points a + bi and s + ti lie on the complex plane, then the formulas to the right can be used to calculate the distance and midpoint between the points.
Khan Academy Practice:
Khan Academy Practice:
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