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...

10 months ago

Answered by Simon, an IB Maths tutor with MyTutor

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


£20 /hr

Anezka E.

Degree: Mathematics (Bachelors) - Kings, London University

Subjects offered: Maths


“About me: I'm hopefully about to start my second year at King's College London. I've thouroughly enjoyed studying maths for many years now and would love to help out a maths lover or hater and hopefully convert the latter into the for...”

MyTutor guarantee

£20 /hr

Martin S.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Economics+ 1 more


“I am a second year economics undergraduate with an interest in maths. I believe that economics is a fascinating subject that is invaluable for personal development even if you aren’t going to pursue it in further education. The fact t...”

MyTutor guarantee

£20 /hr

Daniel E.

Degree: Mathematics (Bachelors) - Edinburgh University

Subjects offered: Maths


“I study Mathemmatics at the University of Edinburgh and I am a real maths enthusiast. I am friendly, calm and patient. I have worked as a volunteer in teaching and worked as tutor in mathematics and french. I have organised a summer s...”

MyTutor guarantee

About the author

Simon T.

Currently unavailable: for regular students

Degree: Natural Sciences Tripos (Masters) - Cambridge University

Subjects offered: Maths, Science+ 4 more

Further Mathematics
-Personal Statements-

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

You may also like...

Posts by Simon

Based on Newton's 3 laws of motion why is linear momentum always conserved?

Take the square root of 2i

Other IB Maths questions

How do i solve simultaneous equation with more than two equations and two unknowns?

Given the function y=f(x), where f(x)=(e^x-e^(-x))/2, find its inverse f'(x).

Solve the equation (2 cos x) = (sin 2 x) , for 0 ≤ x ≤ 3π .

Solve the equation 8^(x-1) = 6^(3x) . Express your answer in terms of ln 2 and ln3 .

View IB Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss