Coordinates defined by a distance (r) from the origin and an angle (θ) from the positive x-axis.

The origin (0,0) in the polar coordinate system.

The positive x-axis in the polar coordinate system, used as the reference for measuring angles.

The radial distance from the pole to the point.

The angle measured counterclockwise from the polar axis.

A number of the form a + bi, where 'a' and 'b' are real numbers, and i is the imaginary unit (√-1).

i = √-1

A plane where the x-axis represents the real part of a complex number, and the y-axis represents the imaginary part.

The distance from the origin to the point representing the complex number in the complex plane.

The angle between the positive real axis and the line connecting the origin to the complex number in the complex plane.

Cartesian: (x, y), uses perpendicular axes | Polar: (r, θ), uses distance and angle from origin

Positive r: Point is in the direction of θ | Negative r: Point is in the opposite direction of θ

Real axis: Represents the real part of a complex number | Imaginary axis: Represents the imaginary part of a complex number

Rectangular: a + bi | Polar: r(cos θ + i sin θ)

Magnitude: Distance from origin | Argument: Angle from positive real axis

Degree: Unit of angle, 360° in a circle | Radian: Unit of angle, 2π radians in a circle

x: Cartesian coordinate | r*cos(θ): Equivalent in polar coordinates

y: Cartesian coordinate | r*sin(θ): Equivalent in polar coordinates

tan⁻¹(y/x): Gives angle in quadrants I or IV | θ: Requires quadrant adjustment for correct angle

Complex number: Has real and imaginary parts (a + bi) | Real number: Only has a real part

$x = r \cdot cos(\theta)$

$y = r \cdot sin(\theta)$

$r = \sqrt{x^2 + y^2}$

$\theta = tan^{-1}(y/x)$ (Adjust quadrant!)

$r(cos \theta + i sin \theta)$

$r = \sqrt{a^2 + b^2}$

$\theta = tan^{-1}(b/a)$ (Adjust quadrant!)

$(r, \theta) = (-r, \theta + \pi)$

$(r, \theta) = (r, \theta + 2\pi k)$

$x = 2cos(7π/6) = -√3$, $y = 2sin(7π/6) = -1$