Express the complex number (1+i)/(1-i) in the form x+iy

First of all calculate the complex conjugate of the denominator. The complex conjugate of (1-i) is 1+i.Now multiply the given complex number by (1+i)/(1+i), note that we are not modifying the starting number since we are just multiplying by 1. The product is (1+i)^2/(1-(i)^2), that is (1+i)^2/2. Finally just calculate (1+i)^2=1+2i+(i^2)=2i, thus (1+i)/(1-i)=2i/2=i=0+1*i.

CM
Answered by Claudio M. Further Mathematics tutor

7289 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

What are Taylor series used for?


Are we able to represent linear matrix transformations with complex numbers?


Find the general solution for the determinant of a 3x3 martix. When does the inverse of this matrix not exist?


A particle is projected from the top of a cliff, 20m above the sea level at an angle of 30 degrees above the horizontal at 20m/s. At what vertical speed does it hit the water?


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