Complex numbers

Concepts

• Complex number 10 exercisesA complex number z is written with two reals, a and b, and the imaginary unit i, which satisfies i^2=-1; a is its real part and b…
• Complex conjugate 10 exercisesThe conjugate of a complex number z, with real part a and imaginary part b, is the complex number bar z that keeps the real part…
• Modulus of a complex number 10 exercisesThe modulus |z| of a complex number z=a+bi is the distance from the point (a,b) to the origin of the complex plane.
• Polar form 10 exercisesThe polar form of a complex number z≠0 expresses it with its modulus r and an argument θ, an angle that z makes with the positive…
• Complex nth root 10 exercisesAn n-th root of a complex number w is a complex number z whose n-th power, with n a positive integer, is w. If w has modulus r an…
• De Moivre's formula 10 exercisesDe Moivre's formula gives the integer power n of a complex number z of modulus r and argument θ: it raises the modulus to the n-t…
• Topology of the complex plane 10 exercisesThe structure that open disks D of center z_0 and radius r give to ℂ; with them one defines when a set of points z is open, close…