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

42896 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How to use the integrating factor?


Write 1 + √3i in modulus-argument form


For a homogeneous second order differential equation, why does a complex conjugate pair solution (m+in and m-in) to the auxiliary equation result in the complementary function y(x)=e^(mx)(Acos(nx)+Bisin(nx)), where i represents √(-1).


How do you sketch the graph of y=(x-1)/(x+1)?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences