Take the square root of 2i

MYTUTOR SUBJECT ANSWERS

Answers / Maths / IB / Take the square root of 2i

743 views

Take the square root of 2i

As with much of complex number the trick here is to change forms to polar representation.

If you think of an argand diagram the number i will be represented as a point straight up on the imaginary axis a distance 2 from the origin.

It can therefore be represented as 2i = 2*e^(iπ/2)

From here it's easy! Just apply the same indices rules that you have grown so familiar with.

2 goes to the square root of 2, e^(iπ/2) goes to e^(iπ/4).

so we have the expression (2i)^(1/2) = (2)^(1/2)*(iπ/4)

And now convert back to standard form!

We know the magnitude is square root 2, and the arguement is π/4. Imagined on the argand diagram this is a line slanting at 45 degrees to the horizontal.

We can use the identity e^(iθ) =cos(θ) + i*sin(θ)

cos(π/4)=sin(π/4)= 2^(-1/2)

Thankfully the square roots of 2 cancel (Careful! they will not allways do this!) Therefore we reach the answer:

(2i)^(1/2) = 1 + i

which is satisfyingly elegant

Simon T. GCSE Further Mathematics tutor, A Level Further Mathematics...

1 year ago

Answered by Simon, an IB Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

44 SUBJECT SPECIALISTS

Diana B. A Level Chemistry tutor, GCSE Chemistry tutor, IB Chemistry ...

View profile

£20 /hr

Diana B.

Degree: Chemistry (Masters) - Imperial College London University

Subjects offered:Maths, Chemistry+ 1 more

“Imperial College London student giving Chemistry, Mathematics and Biology lessons”

MyTutor guarantee

Save profile

Navjyot D. GCSE Economics tutor, A Level Economics tutor, GCSE Maths ...

View profile

£20 /hr

Navjyot D.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Economics+ 3 more

“Warwick Economics Graduate with a passion for helping students reach and exceed their potential.”

MyTutor guarantee

Save profile

Kamil F. A Level Further Mathematics tutor, GCSE Further Mathematics...

View profile

£20 /hr

Kamil F.

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Maths, Physics+ 2 more

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

5.0

2 reviews | 2 completed tutorials

Save profile

See more IB Maths tutors

About the author

View profile

Simon T.

Currently unavailable: for new students

Degree: Natural Sciences Tripos (Masters) - Cambridge University

Subjects offered:Maths, Science+ 4 more

“ Enthusiastic tutor for Maths and Physics; 3rd year Cambridge astrophysicist undergraduate.”

5.0

3 reviews | 10 completed tutorials

Save profile

Version:	3.49.4
Build:	b2e05e7dfef3
Time:	2017-08-18T11:35:22Z

MYTUTOR SUBJECT ANSWERS

Take the square root of 2i

Still stuck? Get one-to-one help from a personally interviewed subject specialist

44 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Simon

Other IB Maths questions

One-to-one help is at your fingertips