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

47155 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Why is the argument of a+bi equal to arctan(b/a)?


Explain the process of using de Moivre's Theorem to find a trigonometric identity. For example, express tan(3x) in terms of sin(x) and cos(x).


Find the complex number z such that 5iz+3z* +16 = 8i. Give your answer in the form a + bi, where a and b are real numbers.


Find the integrating factor of the following first order ODE: dx/dt = -2tx +t.


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