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

44330 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?


Given that k is a real number and that A = ((1+k k)(k 1-k)) find the exact values of k for which A is a singular matrix.


It is given that f(x) = 2sinhx+3coshx. Show that the curve y = f(x) has a stationary point at x =-½ ln(5) and find the value of y at this point. Solve the equation f(x) = 5, giving your answers exactly


How to determine the modulus of a complex number?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences