What is the Argument of Complex Numbers? The Argument of a Complex Number is an angle that is inclined from the real axis towards the direction of the Complex Number which is represented on the Complex plane. We can denote it by "θ" or "φ" and can be measured in standard units "radians". In the complex plane, the x -axis represents the real axis and the y -axis represents the imaginary axis. If we have a complex number in the form z=a+bi z = a + bi, the formula for the magnitude of this complex number is: |z|=\sqrt { { {a}^2}+ { {b}^2}} ∣z∣ = a2 + b2. In this formula, a is our real component and b is our imaginary component. 1. It is undefined. An easy way to see that it would be difficult to define it uniquely is to consider that the argument of a product is the sum of arguments, i.e: arg(z1z2) = arg(z1) + arg(z2) arg ( z 1 z 2) = arg ( z 1) + arg ( z 2) If we consider z1 = 0 z 1 = 0, we find: arg(0) = arg(0) + arg(z2) arg ( 0) = arg ( 0) + arg ( z 2) So therefore The "intuitive" reason you seek, is that any complex number $z$ can be written in function of its argument $\theta$ as follows: $$z = re^{i\theta},$$ where $r$ is the Modulus of a Complex Number. Question. What is the principal argument of The complex number satisfying arg (z + i) = Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial z n+1 = z n 2 + c remains bounded. That is, a complex number, c , is in the Mandelbrot set if, when starting with z 0 = 0 and applying the iteration repeatedly, the absolute value of z n Division of Two Complex Numbers. While dividing a complex number by another non-zero complex number, that is, z1 ÷ z2 = z1 z2 = z1 × 1 z2, z2 ≠ 0r, follow the steps: Step 1: Set up the division problem as a fraction. Step 2: Use the concept of the identity (z1 + z2)(z1- z2) = z21- z22 to rationalize the denominator. Find the modulus and argument of the complex number {eq}z = -2 -2 i {/eq}. Step 1: Graph the complex number to see where it falls in the complex plane. This will be needed when determining the a is the real part of the complex number z, and ; b is the imaginary part of the complex number z. Argument of Complex Number. The angle between the radius vector of a complex number and the positive x-axis is called the argument of a complex number. For a complex number z = a + ib, it is mathematically given by: θ = tan-1 (b/a) What does $\arg(z-z_1)-\arg(z-z_2)=\phi$ represents. Hot Network Questions What range of altitudes would not be fatal for an astronaut falling from height on the moon? zXcBp0E.