Rectangular form is when a complex number is expressed as a combination of a real number and an imaginary number in the form a + bi, where a is the real part and bi is the imaginary part. On the other hand, polar form is when a complex number is expressed in terms of its magnitude (r) and angle (θ) in the form r(cos θ + isin θ).
To convert a complex number from rectangular to polar form, you can use the following formula: r = √(a² + b²) and θ = tan⁻¹(b/a). This will give you the magnitude and angle of the complex number, which can then be expressed as r(cos θ + isin θ).
Yes, you can add or subtract complex numbers in polar form by converting them to rectangular form, performing the operation, and then converting back to polar form. Alternatively, you can use the formula z₁ + z₂ = r₁(cos θ₁ + isin θ₁) + r₂(cos θ₂ + isin θ₂) = (r₁ + r₂)(cos(θ₁ + θ₂) + isin(θ₁ + θ₂)) to add two complex numbers in polar form directly.
To multiply two complex numbers in polar form, you can use the formula z₁z₂ = r₁r₂(cos(θ₁ + θ₂) + isin(θ₁ + θ₂)). To divide two complex numbers in polar form, you can use the formula z₁/z₂ = r₁/r₂(cos(θ₁ - θ₂) + isin(θ₁ - θ₂)).
Yes, you can graph complex numbers in polar form by converting them to rectangular form and plotting them on the complex plane. The magnitude of the complex number will be the distance from the origin, and the angle will determine the direction of the complex number on the plane.