How do I express complex numbers in the form reiθ?

How do I express complex numbers in the form re? Complex numbers have a general form of a+ib, i being imaginary. To answer this it is best shown on an argand diagram. Plot your complex number, then the angle at which the complex expression is plotted is your theta and its distance is "r". 

Example 3+4i

Using pythagaros we find "r": (32+42)1/2=5

Using trigonometry we find "θ": tan-1(4/3)=0.927 Rad

Therefore 3+4i is represented as 5e0.927i

KL
Answered by Kishen L. Further Mathematics tutor

47710 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

A golf ball is hit from horizontal ground with speed 10 m/s at an angle of p degrees above the horizontal. The greatest height the golf ball reached above ground level is 1.22m. Model the golf ball as a particle and ignore air resistance. Find p.


Give the general solution of the second order ODE dy2/d2x - 4dy/dx + 3 = 0


Find the eigenvalues and eigenvectors of the following 3x3 matrix (reading left to right, top to bottom): (1 0 2 3 1 1 2 0 1)


What is the value of x from (x+2)^2=4


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:

© 2026 by IXL Learning