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
10230 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Where does Euler's Formula come from?
Prove by mathematical induction that, for all non-negative integers n, 11^(2n) + 25^n + 22 is divisible by 24
Prove that ∑(1/(r^2 -1)) from r=2 to r=n is equal to (3n^2-n-2)/(4n(n+1)) for all natural numbers n>=2.
It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.