Answers>Maths>IB>Article

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 = 2e^(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 + iwhich is satisfyingly elegant

ST
Answered by Simon T. Maths tutor

7026 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

Solve the differential equation csc(x)*dy/dx=exp(-y), given that y(0)=0. (Typical Math HL paper 3 question, Calculus optional topic)


The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?


A sequence of numbers have the property that x, 12, y, where x > 0, y > 0, form a geometric sequence while 12, x, 3y form an arithmetic sequence. A)If xy = k, find k. B)Find the value of x and y.


Given two functions f and g where f(x)=3x-5 and g(x)=x-2. Find: a) the inverse f^-1(x), b) given g^-1(x)=x+2, find (g^-1 o f)(x), c) given also that (f^-1 o g)(x)=(x+3)/3, solve (f^-1 o g)(x)=(g^-1 o f)(x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences