Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Julia sets Next Document: Logistic equation See reader questions & answers on this topic!  Help others by sharing your knowledge Q8a: How does complex arithmetic work? A8a: It works mostly like regular algebra with a couple additional formulas: (note: a,b are reals, x,y are complex, i is the square root of 1) Powers of i: i^2 = 1 Addition: (a+i*b)+(c+i*d) = (a+c)+i*(b+d) Multiplication: (a+i*b)*(c+i*d) = a*cb*d + i*(a*d+b*c) Division: (a+i*b)/(c+i*d) = (a+i*b)*(ci*d)/(c^2+d^2) Exponentiation: exp(a+i*b) = exp(a)(cos(b)+i*sin(b)) Sine: sin(x) = (exp(i*x)exp(i*x))/(2*i) Cosine: cos(x) = (exp(i*x)+exp(i*x))/2 Magnitude: a+i*b= sqrt(a^2+b^2) Log: log(a+i*b) = log(a+i*b)+i*arctan(b/a) (Note: log is multivalued.) Log (polar coordinates): log(r*e^(i*theta)) = log(r)+i*theta Complex powers: x^y = exp(y*log(x)) DeMoivre's theorem: x^a = r^a * [cos(a*theta) + i * sin(a*theta)] More details can be found in any complex analysis book. Q8b: How does quaternion arithmetic work? A8b: Quaternions have 4 components (a+ib+jc+kd) compared to the two of complex numbers. Operations such as addition and multiplication can be performed on quaternions, but multiplication is not commutative.. Quaternions satisfy the rules i^2=j^2=k^2=1, ij=ji=k, jk=kj=i, ki=ik=j. See: http://www.dtek.chalmers.se/Datorsys/Project/qjulia/index.html QJulia page (quaternions) (Henrik Engstrvm) User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Fractal Frequently Asked Questions and Answers Previous Document: Julia sets Next Document: Logistic equation Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: stepp@marshall.edu
Last Update March 27 2014 @ 02:11 PM
