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
SL
Answered by Samuel L. • Further Mathematics tutor
4663 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸What does it mean if two matrices are said to be commutative?
Using a Suitable substitution or otherwise, find the differential of y= arctan(sinxcosx), in terms of y and x.
f(x)=ln(x). Find the area underneath the curve f(x) between 1 and 2.
Prove that 1+4+9+...+n^2 = n(n+1)(2n+1)/6.