What are the different forms of complex numbers and how do you convert between them?

Complex numbers have three primary forms: the general form, z=a+ib; the polar form, z=r(cosθ+isinθ); and the exponential form, z=rexp(iθ). To convert from the general form to either form you need to find r and θ: r is known as the modulus of z, by referring to an Argand diagram the modulus of z is the length of the line z=a+ib, so to find the modulus you use Pythagoras. θ is called the argument of z and is found by looking at the trigonometry of the line; the two components of z are the opposite and adjacent so you can use tanθ=b/a and rearrange for θ. To work in reverse it is best to use the polar form of the complex number as you simply set a=rcosθ and b=rsinθ.

PL
Answered by Peter L. Further Mathematics tutor

37299 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution of the differential equation d^2y/dx^2 - 5*dy/dx + 4y = 2x


Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)


explain the eigenvalue problem


Express the complex number (1+i)/(1-i) in the form x+iy


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning