Z² + (1+i)Z + (5-i4) = 0

That's a quadratic in Z.  Use the quadratic formula:










Replace i² by (-1)







Now we have to find the square root by DeMoivre's theorem:



Put -20+18i in polar form











root(4,724)cis(expr(tan^"-1"(-0.9))/2)




or decimal approximation (and you can get it immediately with a TI-84
straight from the original equation):

Z = .4291964334+1.92144709i,  -1.429196433-2.92144709i

Edwin