When a complex number [tex]\( z \)[/tex] is written in its polar form as [tex]\( z = r(\cos \theta + i \sin \theta) \)[/tex], we focus on the representation involving [tex]\( r \)[/tex] and [tex]\( \theta \)[/tex].
Here, [tex]\( r \)[/tex] is a nonnegative real number, and it represents the distance from the origin to the point in the complex plane corresponding to the complex number [tex]\( z \)[/tex]. This measurement of distance is crucial in understanding how far a complex number is from the origin regardless of its direction (angle [tex]\( \theta \)[/tex]).
Therefore, the nonnegative number [tex]\( r \)[/tex] is referred to as the magnitude or modulus of the complex number [tex]\( z \)[/tex].
