Answers>Maths>IB>Article

Find a and b (both real) when (a+b*i)^2=i.

Every complex number has a real and imaginary part. For the complex number z=a+bi the notation for real and imaginary parts respectively are Re(z)=a and Im(z)=b. If you know this, many complex algebra equations will become much simpler to solve.

In this specific case, firstly consider LHS, giving z=a2+ 2abi+(ib)2=(a2-b2)+(2ab)*i. (since i2=-1). Consequently, Re(z)=a2-b2 and Im(z)=2ab. Next consider the RHS, write its real and imaginary parts: Re(i)=0 and Im(i)=1. Equate LHS and RHS, getting a system of equations:  a2-b2=0 and 2ab=1.
The solutions are a=-1/sq(2), b=1/sq(2) and a=1/sq(2), b=-1/sq(2).

UA
Answered by Urte A. Maths tutor

1534 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

How should I approach a proof by induction question?


How to I solve system of simultaneous equations (3x3)?


Solve x^2 + 2x = 48 for all values of x


Solve: 1/3 x = 1/2 x + (− 4)


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