Properties of argument of complex number and basic properties explained
In this video explained Properties of argument of complex number and basic properties explained step by step class 11 mathematics. The argument of a complex number is the angle that the line connecting the origin and the complex number makes with the positive x-axis in the complex plane. The argument of a complex number z = a + bi (where a and b are real numbers) is denoted by arg(z) or θ and it can be found using the inverse tangent function
θ = arctan(b/a)
The properties of the argument of a complex number are as follows
The argument of a complex number is always between -π and π.
The argument of a real number is 0 if the real number is positive and π if the real number is negative.
The argument of a complex number with a positive imaginary part is in the first or fourth quadrant. The argument of a complex number with a negative imaginary part is in the second or third quadrant.
The argument of a complex number z = a + bi is equal to the argument of its conjugate of z = a - bi.
The argument of a product of two complex numbers is equal to the sum of the arguments of the individual complex numbers.
The argument of a quotient of two complex numbers is equal to the difference of the arguments of the individual complex numbers.
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