# Logarithmic functions and polar form of complex numbers

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1/ If the amplitude ratio, N in decibels, of an electrical system is given by the formula.

N = 10log

And the power is given by

P =

Show that for matched input and output resistances the output voltage Vo is related to the input voltage Vi by:

Vo = Vi10

If N is increased by 6db, show that the output voltage is approximately doubled for the same input. Following to polar form giving the arguments in degrees

2/ convert the Following to polar form giving the arguments in degrees:

a/ 4 - j2.4

b/ -5.1 + j1.7.

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##### Solution Summary

I have answered two questions. One involves the logarithmic formula for amplitude ratio. The other involves the writing of complex numbers and their polar form.

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Answer:

It is given that P = V^2 / R

Let Po = Vo^2 / R and Pi = Vi^2 / R

Substituting in (1),

N = 10 log[(Vo^2 / R) / Vi^2 / R]

N = 10 log[(Vo^2 / Vi^2 ]

N = 10 log (Vo /Vi)^2 = 20 log (Vo/Vi)

N = 20 log ...

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