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Translation of complex numbers

Lecture



Translate the current set in time form i (t) = 141 sin (ɷt + 90 °) into a complex form: exponential and algebraic.

Decision:
amplitude value of current Im = 141 A
+ 90 ° - the initial phase of the current.

We write the complex current in exponential form:
Complex current amplitude

  Translation of complex numbers

current value complex

  Translation of complex numbers

We translate into algebraic form using Euler's formula

  Translation of complex numbers

Task 2

Algebraic voltage is specified.

  Translation of complex numbers

Transfer to a temporary form.

Decision:
consider the stress vector on the complex plane

  Translation of complex numbers

It turns out that the vector is in the third quarter of the complex plane. This means that the initial phase of the angle is from 180 ° to 270 °, i.e. add 180 ° to the resulting angle

  Translation of complex numbers

The value of the voltage module is determined by the Pythagorean theorem

  Translation of complex numbers

Answer: u (t) = 40 sin (ɷt + 225 °)

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Electrical Engineering, Circuit design

Terms: Electrical Engineering, Circuit design