MYTUTOR SUBJECT ANSWERS

266 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...

9 months ago

Answered by Simon, an IB Maths tutor with MyTutor


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

23 SUBJECT SPECIALISTS

£20 /hr

Kyle R.

Degree: Mathematics (Masters) - Oxford, Corpus Christi College University

Subjects offered: Maths, Further Mathematics + 2 more

Maths
Further Mathematics
.STEP.
.MAT.

“Hi! I'm Kyle, a 2nd year Oxford undergraduate studying Maths at Corpus Christi College. I aim to be an understanding and friendly face, whilst being thorough with the material I cover. I've acheived A* grades in Maths, Further Maths a...”

£20 /hr

Matt E.

Degree: Molecular Biology (Doctorate) - Queen's, Belfast University

Subjects offered: Maths, Science+ 4 more

Maths
Science
Human Biology
Chemistry
-Personal Statements-

“I am a first year PhD student at the School of Biological Sciences at Queen's University, Belfast, having graduated with a first class honours degree in Biology from QUB. My research focuses on the molecular mechanisms underpinning th...”

MyTutor guarantee

£22 /hr

Hanumanth Srikar K.

Degree: Maths and Economics (Bachelors) - LSE University

Subjects offered: Maths, German+ 3 more

Maths
German
Further Mathematics
Economics
Chemistry

“Hanumanth Srikar Karri - London School of Economics”

About the author

Simon T.

Currently unavailable: for regular students

Degree: Natural Sciences Tripos (Masters) - Cambridge University

Subjects offered: Maths, Science+ 4 more

Maths
Science
Physics
Further Mathematics
Chemistry
-Personal Statements-

“Hey, I'm a first year undergraduate at Cambridge studying Natural Science”

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

Take the square root of 2i

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

How do you calculate the probability P(X < x) for a normally distributed random variable X?

What are the key elements to include in your Math assignment?

View IB Maths tutors

Cookies:

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

mtw:mercury1:status:ok