Prove. Problem is attached in following file.
Show that if z0 is an nth root of unity(z0 is not equal to 1) then 1+z0+z0^2+...+z0^(n-1)=0. Hence show that cos(2Pi/1998)+cos(4Pi/1998)+...+cos(2Pi*1997/1998)=-1
Given u = y^3 - 3x^2y, find f(z) = u + iv such that f(z) is analytic. The solution is detailed and well presented.
Find the existence of a limit in a complex value function. Please see the attached file.
Given a function w = f(z) = z^2 then decompose f(z) into its real and imaginary parts.
Write the simplest polynomial equation that has roots 1+i and -1.
Solve (find the roots): (2x-3/x) + (5x-3/x^2) - (2x^2) + (x-6/x^3) = 2
Find the trigonometric form of the complex number where 0 <= theta < 2pi on the equation: r= 1/2 - [(sqrt(3)/2)i]
Find the roots. X^3 + 4*x^2 +6x -2 =0
Find all the zeros (both real and complex) of f(x)= x^5 - 3x^4 + 12x^3 - 28x^2 + 27x -9
1. Without solving the equation determine the number of roots (real, different, same, imaginary): a) 2x^2+7x-14=0 b) do the same for 2x^2-3x+10=0 c) e^2x+5=ln 125
What steps should be taken to solve complex order of operation equations?