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)

JL
Answered by Jamie L. Further Mathematics tutor

12944 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Differentiate arcsin(2x) using the fact that 2x=sin(y)


What is the root of i? give all solutions


Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n


Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning