Currently unavailable: for new students

Degree: Mathematics (Bachelors) - Cambridge University

Second year Cambridge maths undergraduate looking to help A-Level Maths and physics students, and also STEP, AEA or MAT.

#### Subjects offered

SubjectQualificationPrices
Further Mathematics A Level £22 /hr
Maths A Level £22 /hr
Physics A Level £22 /hr
.STEP. Uni Admissions Test £25 /hr

#### Qualifications

MathematicsA-levelA2A*
Further MathematicsA-levelA2A*
PhysicsA-levelA2A*
 CRB/DBS Standard No CRB/DBS Enhanced No

#### Ratings and reviews

4.5from 19 customer reviews

Nancy (Parent) June 9 2016

Edi is very knowledgeable in Maths and Further maths! Highly recommend him!

Nancy (Parent) June 10 2016

An excellent tutor, great help! Thank you so much!

Nancy (Parent) June 14 2016

Nancy (Parent) April 13 2016

An excellent tutor! Thank you!
See all reviews

### Find the nth roots of unity.

Let me rephrase this question slightly:   "Find all the roots of the equation x^n - 1 = 0." We know by the fundamental theorem of algebra that an nth degree polynomial has *exactly* n roots. So the excersice has now been reduced to something as simple as: can you find n different numbers  (ca...

Let me rephrase this question slightly:

"Find all the roots of the equation x^n - 1 = 0."

We know by the fundamental theorem of algebra that an nth degree polynomial has *exactly* n roots. So the excersice has now been reduced to something as simple as: can you find n different numbers  (call them x) such that  x^n = 1.

Well we know 1 works. Let us call it eoiπ from now on. We still need to find the (n-1) other roots. The key to this is using the fact that 1 = eoiπ, e2, e4, ... So long as our number when raised by n goes to any one of these numbers, we are done. Well, we can see e2iπ/n does the job, and we can also see e4/n does the job, so more generally e2riπ/n does the job for all positive integer r. Now we just need to find n of these numbers that are actually distinct (recall that there are infinitely many different ways of writing a number depending on how you write its argument, so while two numbers may be written differently they will actually be the same).
But fear not! If we look at e2riπ/n for 0 <= r < n, and r an integer, these are all distinct! (If they were not distinct then we could prove that eix = 1 for an x such that 0 < x < 2π, which is false).

see more

2 years ago

705 views
Send a message

All contact details will be kept confidential.

To give you a few options, we can ask three similar tutors to get in touch. More info.

Still comparing tutors?

How do we connect with a tutor?

Where are they based?

How much does tuition cost?

How do tutorials work?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.