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
4476 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4
Explain the process of using de Moivre's Theorem to find a trigonometric identity. For example, express tan(3x) in terms of sin(x) and cos(x).
How to integrate ln(x)?
Solve x^3=1 giving all the roots between -pi<=theta<=pi in exponential form