Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter

    Okay, I had a question where I was given a simple complex number in the form a+bi, and asked to put it in polar form. So I changed it to \sqrt{a^2+b^2}[cos(\theta )+isin(\theta )], \theta =\frac{b}{a}. However the answer was in the form of \sqrt{a^2+b^2}e^i{\theta }, \theta =\frac{b}{a}. I was under the impression that this was the "Euler form".

    Can someone just clear up which form is which so I am not confused from now on !

    Polar form just means in terms of it's distance from the origin (its 'radius') and its angle from 1. Both of the forms you have given would qualify as some kind of polar form but writing it as an exponent of e is the most common way since it has the same amount of information and is easier to write.

    I would always write a complex number in the form  r\ cis(\theta), where r is the modulus of the complex number and  cis(\theta) is another way of saying  cos(\theta)+i\ sin(\theta) . That's polar form to me.

    I almost never use Euler's formula unless I'm proving its validity by the Maclaurin series.

    At degree level I'd say re^{i\theta} is very much the canonical form for a polar representation.

    I would agree that re^{i\theta} is much more standard than r(\cos \theta + i \sin \theta) or the quite ugly r \operatorname{cis}\theta.

    However, as usual, if you are answering a question from your course, then what your lecturer/teacher means by 'polar form' will be contained within the content of your course i.e. will have been mentioned in lessons/lectures/the book/lecture notes etc. So the first call would be to reexamine those. I am nearly sure, however, that if you have covered Euler's formula then your teacher/lecturer will either:

    a) decree re^{i\theta} as standard polar form or
    b) accept either way of writing it.
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you rather give up salt or pepper?
    Useful resources

    Make your revision easier


    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here


    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.