Anzeige Argument of a Complex Number CalculatorCalculate the argument and absolute value of a complex number. The argument of a complex number is the direction of the number from the zero point or the angle to the real axis. This function is sometimes also referred to as atan2(a,b). The direction angle is usually given in radians, where 0 corresponds to the direction of the positive x-axis, π/2 is then vertically upwards and so on. The absolute value is the distance of the complex number from the zero point.
The absolute value is calculated according to the Pythagorean theorem: |a+bi|² = a² + b², |a+bi| is then the positive root of this value. Please enter the two values a and b of a complex number in the form a+bi. The argument is calculated as a radian and as a multiple of the number pi, π. The corresponding angle is also output in degrees, with 90 degrees being vertically upwards, i.e. π/2. The last value calculated is the absolute value, i.e. the length of the distance from the zero point to the value on the complex plane. Example: the argument of 2+3i is 0.98279372, or 0.31283296 times π. The absolute value of this complex number is 3.60555128. The angle is about 56.3 degrees, this is mainly used for visualization, in this case it goes to the top right with a little more to the top than to the right. Argument and absolute value are needed to represent a complex number in polar form and exponential form. Their representation is more complicated, but is advantageous for some calculations. The number zero cannot be represented in polar form or in exponential form because the argument is then undefined. |