Translation of complex numbers

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



current value complex



We translate into algebraic form using Euler's formula



Task 2

Algebraic voltage is specified.



Transfer to a temporary form.

Decision:
consider the stress vector on the complex plane



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



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



Answer: u (t) = 40 sin (ɷt + 225 °)