periodic functions of period 2ˇ. We define the principal argument of a complex number to be the angle with a specified range described below: Definition 1.7 (Principal Argument). Given a complex number z, the principal argument of z, denoted by Arg(z), is defined to be the angle 0 2( ˇ;ˇ] such that: z= jzj(cos 0 + isin 0): For example, 1 p The angle θ which OP makes with the positive direction of x-axis in anticlockwise sense is called the argument or amplitude of complex number z. It is denoted by arg (z) or amp (z). From Figure, we have. t a n θ = P M O M = y x = I m ( z) R e ( z) θ = t a n − 1 ( y x) This angle θ has infinitely many values differing by multiples of 2 π The argument function is denoted - arg(z), z indicates the complex number i.e "z=x+iy. How to Find Arguments of Complex Numbers. Steps to find arguments of complex numbers: Find both real as well imaginary parts from the complex number given. Then denote them as X and Y. If we let h → 0 h → 0 along the line (or ray) Arg(z) = Arg(z0) Arg ( z) = Arg ( z 0), this expression clearly tends to 0 0. This at leasts shows that f f cannot be differentiable at any open set: If it were, the derivative would be zero and f f would be contant on that open set. Obviously Arg(z) Arg ( z) is not constant on any open set. The principal value \(Arg(z)\) of a complex number \(z=x+iy\) is normally given by \(\Theta =arctan(\frac{y}{x})\), where \(y/x\) is the slope, and arctan converts slope to angle. This is a real number, but this tells us how much the i is scaled up in the complex number z right over there. Now, one way to visualize complex numbers, and this is actually a very helpful way of visualizing it when we start thinking about the roots of numbers, especially the complex roots, is using something called an Argand diagram. .

what is arg z of complex number