Complex Number Calculator: Convert to a+bi Form

Understanding the a+bi Form of a Complex Number

Complex numbers are expressed in two primary formats: rectangular form and polar form.

The rectangular form, written as a + bi, identifies a point (a, b) on the complex plane. Here, 'a' is the real component and 'b' is the imaginary component.

The polar form describes the number using magnitude and angle: r × exp(φi). Here, 'r' is the modulus (distance from origin) and 'φ' is the argument (angle with the positive real axis).

A Simple Guide: Converting from Polar to Rectangular Form

To convert a polar form complex number, z = r × exp(iφ), into rectangular a+bi form, apply these formulas derived from trigonometric relationships on the complex plane.

a = r × cos(φ)
b = r × sin(φ)

Calculate the real part 'a' using a = r × cos(φ), and the imaginary part 'b' with b = r × sin(φ).

How to Use a Complex Number Calculator

Using an online a+bi form calculator is efficient. Input the polar coordinates: the magnitude (r) and the phase angle (φ). You can typically choose the angle unit (radians or degrees). The calculator then instantly processes the data and displays the resulting real part 'a' and imaginary part 'b' in the final a + bi format.

Frequently Asked Questions (FAQs)