How do I find the square root of a complex number?
Say you want to find the square root of the complex number 3+2i.
We can assume that the answer we want will be in the form a+bi.
It follows then, that you can also write 3+2i as (a+bi)2.
Expanding this gives us 3+2i = a2+2abi-b2
Then all we need to do is compare the coefficients of the imaginary and real parts: i.e. 3 = a2-b2 and 2 = 2ab.
Solve these 2 simultaneous equations to get a =1.8 and b = 0.56 (ignore any imaginary solutions for a and b - they have to be real).
Therefore the square root of 3+2i is 1.8+0.56i. You can check this by squaring our solution and you'll get back to 3+2i (or near enough due to rounding).
DC
Answered by Dan C. • Further Mathematics tutor
10271 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸For a homogeneous second order differential equation, why does a complex conjugate pair solution (m+in and m-in) to the auxiliary equation result in the complementary function y(x)=e^(mx)(Acos(nx)+Bisin(nx)), where i represents √(-1).
What are imaginary numbers and why do we use them?
3 points lie in a plane; P1=i+2j+3k, P2=-3i+5j+2k, P3=i+2j+k. Find the Cartesian equation of the plane
How can the integrating factor method be derived to give a solution to a differential equation?