Polar Coordinates

Front

What are polar coordinates?

Back

Polar coordinates are a two-dimensional coordinate system where each point is determined by a distance from a reference point (the origin) and an angle from a reference direction (usually the positive x-axis).

Front

How do you convert Cartesian coordinates (x, y) to polar coordinates (r, θ)?

Back

Front

What is the absolute value of a complex number?

Back

Front

What quadrant does the point (x, y) = (2, 3) lie in?

Back

The point (2, 3) lies in Quadrant 1, where both x and y are positive.

Front

What is the polar coordinate representation of the point (1, 0)?

Back

The polar coordinate representation is (1, 0), where r = 1 and θ = 0.

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

To multiply, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2, and remember that i^2 = -1.

Front

What is the polar coordinate of the point (√3, 1)?

Back

Front

What is the angle θ in polar coordinates when the point is in Quadrant 2?

Back

Front

What is the relationship between polar coordinates and complex numbers?

Back

Polar coordinates can represent complex numbers as r(cos θ + i sin θ), where r is the modulus and θ is the argument.

Front

How do you find the angle θ for the point (-4, 3) in polar coordinates?

Back