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

Think about the point a+bi on the complex plane. Specifically, a is how far along the x (real) axis, and b is how far up the y (imaginary) axis the point is. If you draw a line connecting the origin and the point a+bi then notice that you've constructed a triangle with sides a, b, and sqrt(a^2+b^2). Recall that tan of an angle = opp/adj, applying this to the triangle gives that the angle between the x-axis and the line from the origin is equal to arctan(b/a). This is exactly what the argument of a complex number is, the angle between the x-axis and the line connecting the number and the origin.

MS
Answered by Martin S. Further Mathematics tutor

12470 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

The ODE mx'' + cx' + kx = 0 is used to model a damped mass-spring system, where m is the mass, c is the damping constant and k is the spring constant. Describe and explain the behaviour of the system for the cases: (a) c^2>4mk; (b) c^2=4mk; (c) c^2<4mk.


write the sum cos(x)+cos(2x)+...+cos(nx) as a quotient only involving sine and cosine functions


Simplify (2x^3+8x^2+17x+18)/(x+2)


The curve C has parametric equations x=cos(t)+1/2*sin(2t) and y =-(1+sin(t)) for 0<=t<=2π. Find a Cartesian equation for C. Find the volume of the solid of revolution of C about the y-axis.


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