How to multiply and divide by complex numbers

Multiplying and dividing by complex numbers is very similar to how you have learned how to multiply and divide surds (numbers with a rational and irrational part) in GCSE and early A-Level. Take two complex numbers, written a+bi and c+di. To multiply together, treat i as you would treat x with multiplication of an algebraic expression. The only difference is remembering that with complex numbers, i^2 = -1. So replace your i^2 term with -1 and simplify.For division, remember how you treat the denominator with surds. For (a+bi)/(c+di), we take what is known as the conjugate of the denominator, c-di. This, when multiplying through the numerator and denominator, will cancel out the complex part in the denominator, leaving our number will a complex numerator and real denominator. This is a much more useful form to have for a complex number, as it makes it easier to perform operations and to visually examine the number.

LC
Answered by Louis C. Further Mathematics tutor

2298 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)


Convert the general complex number z=x+iy to modulus-argument form.


Solve for z in the equation sin(z) = 2


Find a vector that is normal to lines L1 and L2 and passes through their common point of intersection where L1 is the line r = (3,1,1) + u(1,-2,-1) and L2 is the line r = (0,-2,3) + v(-5,1,4) where u and v are scalar values.


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