Find phasor form of voltage v and current i compute complcx

Question

1. a. Find real part and imaginary part of sin (i5+ π/3)

b. Find real pan and imaginary part of cosh(4 - 3i)

2. a. Find all solutions of sin z = 100.

b. Find all solutions of sinh z = -i.

3. Convert time varying functions i₁ = 6 cos (377t - π/3) and i₂ = -9 sin (377t + π/4) into complex phasors I₁ and I₂.

b. We know i₁ + i₂ = A cos (377t + Φ). Find A and Φ (in radian) with the phasor method.

c. Complex power is defined as P = |I₁ + I₂|² (R + iωL) where I₁ and I₂. arc phasors in a) and R =100 and L= 1. Compute P in polar form.

4. a. Voltage v(t) = 10 sin (200 t + 60^o) (v) and current i(t) = 20 cos (200t - 45^o) (A)

i. Find phasor form of voltage (V) and current (I).

ii. Compute complcx power P = VI and average power P_avg = Re{P}/2.

b. Find the time varying cos function for the following phasors that have angular frequency of to ω:

i. (6 ∠65^o)/(3+i2)
ii. {1/(1+i2.5)} + 1 + i2.5.