Where z is a complex number, what is the cartesian form of |Z-2+3i| = 1?

Z is simply a general complex number, which can be written as Z = x+iyHere |Z-2+3i| = 1 can be written as |Z-(2-3i)| = 1, which is just an expression for every Z whose distance from the point (2,-3i) is equal to 1.We can solve this by recalling that Z = x+iy, and so we can seperate the real and imaginary parts in the modulus function. i.e. 1 = |(x-2) + i(y+3)| Evaluating the modulus now becomes simple as we calculate the magnitude using pythagoras. This Yields:12 = (x-2)2 + (y+3)2 , which is the cartesian form!we recognise this as the equation of a circle, with centre (2,-3) and radius 1. 

MH
Answered by Mark H. Maths tutor

9116 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you find dy/dx for a set of parametric equations?


Find the value of dy/dx at the point where x = 2 on the curve with equation y = x^ 2 √(5x – 1).


Integrate the function x(2x+5)^0.5


How do you do simple integration?


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