A+Bi Form Calculator
Express complex numbers in a+bi standard form and calculate the magnitude. Free online complex number calculator with instant results and formula breakdown.
About This Calculator
The A+Bi Form Calculator converts complex numbers to their standard rectangular form and computes the magnitude. Complex numbers in a+bi form consist of a real part 'a' and an imaginary part 'b', where i = sqrt(-1).
The magnitude of a+bi is calculated as |a+bi| = sqrt(a^2 + b^2), representing the distance from the origin in the complex plane.
Frequently Asked Questions
What is a+bi form?
The a+bi form is the standard rectangular form of a complex number where 'a' is the real part and 'b' is the imaginary part. For example, 3+4i has real part 3 and imaginary part 4. The 'i' represents the imaginary unit sqrt(-1).
How do you calculate the magnitude of a+bi?
The magnitude (modulus) of a complex number a+bi is calculated as |a+bi| = sqrt(a^2 + b^2). This represents the distance from the origin to the point (a,b) in the complex plane. For example, |3+4i| = sqrt(9+16) = sqrt25 = 5.
What is the difference between a+bi and polar form?
The a+bi form (rectangular form) uses Cartesian coordinates (a,b) to represent a complex number. Polar form uses magnitude r and angle theta: r(costheta + i sintheta) or re^(itheta). The rectangular form is better for addition/subtraction, while polar form is better for multiplication/division.