Question

Obtain the time domain equivalent for the following phasors:

a. j
b. e−ʲπ/⁴e−ʲπ/²
c. (1−j)eʲπ/²
d. ln(2+j)

Answer 1

To obtain the time domain equivalent for the given phasors, they can be converted to exponential form. Phasor j can be represented as e^j1t. Phasor e^-jπ/4e^-jπ/2 can be represented as e^-j(3π/4)t. Phasor (1-j)e^jπ/2 can be represented as e^j(π/2)t - je^j(π/2)t. Phasor ln(2+j) can be represented as e^ln(√5)e^jarctan(2/1).

Step-by-step explanation:

The time domain equivalent for the given phasors can be obtained by converting them to exponential form.

a. The phasor j can be written as j = 0 + j1. In exponential form, this can be represented as ej1t.

b. The phasor e-jπ/4e-jπ/2 can be written as e-j(π/4 + π/2). In exponential form, this can be represented as e-j(3π/4)t.

c. The phasor (1-j)ejπ/2 can be written as 1ejπ/2 - jejπ/2. In exponential form, this can be represented as ej(π/2)t - jej(π/2)t.

d. The phasor ln(2+j) can be converted to exponential form by applying the Euler's formula. The real part is ln(√5) and the imaginary part is arctan(2/1). In exponential form, this can be represented as eln(√5)ejarctan(2/1).