Why is impedance taken as a complex quantity?

Question

Impedance is denoted as magnitude(angle) in polar form and as resistance+j(reaciance) in rectangular form

Answer 1

Simplifies the mathematics. You can apply Ohm's law without worrying about whether the impedances are resistive or reactive.

Answer 2

Because it has a 'real', resistive component, and an 'imaginary' reactive (capcitive or inductive) component. It is a 2-dimensional quantitiy, so it is represented by a complex (2-dimensional) number.

The math gets easier, when you treat the reactive component as an imaginary number, rather than as a real number in the vector impedance.

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