This video explains the modulus and argument of a complex number.
It defines the modulus as the length or magnitude of the complex number when plotted on an Argand diagram. It details how to calculate the modulus using the formula |z| = √(a² + b²), where 'a' represents the real part and 'b' represents the imaginary part of the complex number, visualized as the sides of a right-angled triangle, with the modulus being the hypotenuse.
The video then defines the argument of a complex number as the angle (θ) it makes with the positive real axis on the Argand diagram. It emphasizes that θ is restricted to the range where θ is strictly greater than -π and less than or equal to π.
The video explains the sign convention for θ: A counter-clockwise rotation from the positive real axis (first and second quadrants) corresponds to a positive θ, while a clockwise rotation (third and fourth quadrants) corresponds to a negative θ.
Finally, the video reinforces these concepts by working through four examples, each featuring a complex number in a different quadrant of the Argand diagram, to demonstrate the calculation of modulus and argument.