How is impedance in polar form converted to an equivalent admittance?

Admittance (Y) is the mathematical reciprocal of impedance (Z). When working with complex numbers in polar form, an impedance is written as a magnitude (Z) and an angle (θ). To find the reciprocal of a number in polar form, you divide 1 by the magnitude (1/Z) and subtract the original angle from zero (0 - θ), which simply changes its sign. Therefore, the equivalent admittance has a magnitude of 1/Z and an angle of -θ. Common distractors suggest taking the reciprocal of the angle or changing the sign of the magnitude. These operations are mathematically incorrect for complex numbers; a magnitude must always remain a positive distance from the origin.