Find the square root of complex number 3 + 4i

Strategy: write down an equation satisfied by the square root, and solve it algebraically.  Method:  square root x+iy  satisfies (x+iy)2 = 3 + 4i. Expand: x2-y2 +2xyi = 3+4i. Comparing coefficients gives:   x2-y2 =3 and 2xy =4. Then substitute y:  x2 -4/x2 = 3. Rearrange to get quadratic in x2 : (x+1)(x2 -4) = 0. x can't be imaginary (by definition) so x= +/- 2. Plug in to equation 2xy = 4, get y = +/- 1. So square root is +/- (2+i).

Related Further Mathematics A Level answers

All answers ▸

Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions


A useful practice: how to determine the number of solutions of a system of linear equations beforehand


Use de Moivre’s theorem to show that, (sin(x))^5 = A sin(5x) + Bsin(3x) + Csin(x), where A , B and C are constants to be found.


What are differential equations, and why are they important?


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