## Impedence

The
impedance Z of a resistance R in series with a reactance X is:

Z = R + jX

**
Rectangular
and polar forms of impedance Z:
Z = R + jX = (R ^{2} + X^{2})^{½}Ðtan^{-1}(X
/ R) = |Z|Ðf
= |Z|cosf
+ j|Z|sinf
**

Addition
of impedances Z_{1} and Z_{2}:

Z_{1} + Z_{2} = (R_{1} + jX_{1}) + (R_{2}
+ jX_{2}) = (R_{1} + R_{2}) + j(X_{1} + X_{2})

Subtraction
of impedances Z_{1} and Z_{2}:

Z_{1} - Z_{2} = (R_{1} + jX_{1}) - (R_{2}
+ jX_{2}) = (R_{1} - R_{2}) + j(X_{1} - X_{2})

Multiplication
of impedances Z_{1} and Z_{2}:

Z_{1} * Z_{2} = |Z_{1}|Ðf_{1}
* |Z_{2}|Ðf_{2}
= ( |Z_{1}| * |Z_{2}| )Ð(f_{1}
+ f_{2})

Division
of impedances Z_{1} and Z_{2}:

Z_{1} / Z_{2} = |Z_{1}|Ðf_{1}
/ |Z_{2}|Ðf_{2}
= ( |Z_{1}| / |Z_{2}| )Ð(f_{1}
- f_{2})

In
summary:

- use the rectangular form for addition and subtraction,

- use the polar form for multiplication and division.