Find the square roots of 2 + isqrt(5)

Since we’re finding the square roots of 2 + isqrt(5) then (x+iy)^2 = 2 + isqrt(5)Thereforex^2 + 2ixy - y^2 = 2 + isqrt(5)Take real and imaginary parts it followsx^2 - y^2 = 2 and 2ixy = isqrt(5)solving this simultaneous equation for x and yx = +- sqrt(10)/2 and y = +- sqrt(2)/2So, answering the question, the square roots of 2 + isqrt(5) are+- sqrt(10)/2 +- isqrt(2)/2

Related Further Mathematics A Level answers

All answers ▸

When using the method of partial fractions how do you choose what type of numerator to use and how do you know how many partial fractions there are?


How can you find the two other roots of a cubic polynomial if you're given one of the roots (which is a complex number)?


How can the integrating factor method be derived to give a solution to a differential equation?


Prove by mathematical induction that, for all non-negative integers n, 11^(2n) + 25^n + 22 is divisible by 24


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