Find the square root of i

When dealing with powers of complex numbers, always start by putting the quantity into exponential form.

i has a magnitude of and an argument of π/2. Using Euler's formula,

i = exp(iπ/2)

Now the expression is in exponential form, taking the square root is easy, using basic exponential math.

sqrt(i) = (exp(iπ/2))^(1/2) = exp(iπ/4)

This quantity has a modulus of 1 and an argument of π/4. Using Euler's formula again,

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

Related Further Mathematics A Level answers

All answers ▸

What is a complex number?


Show that the square of any odd integer is of the form (8k+1)


Solve the inequality x^3 + x^2 > 6x


Find the complementary function to the second order differential equation d^2y/dx^2 - 5dy/dx + 6x = x^2


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences