An aircraft P flying at a constant height has a velocity of (300+j400)km/h. Another aircraft Q at the same height has a velocity of (200+j500) km/h.

Determine a)the velocity of P in relation to Q.
b) the velocity of Q in relation to P

Ok, you need to learn to do these. We will be happy to critique your reasoning or work.

Velocityrelativez + VelocityZrelativeground= velocityrelativetoground

so memorize that. In this case it says

velocityPrelA+VelocityQrelground=VelocityPrelativeGround

or
VelociytPrelQ+(200+j500)=300+j400

To determine the velocity of aircraft P in relation to aircraft Q, we need to subtract the velocity of aircraft Q from the velocity of aircraft P.

a) Velocity of P in relation to Q:
Velocity of P - Velocity of Q = (300+j400) - (200+j500)

To subtract complex numbers, we subtract the real parts and the imaginary parts separately:

Real part: 300 - 200 = 100
Imaginary part: 400 - 500 = -100

Therefore, the velocity of P in relation to Q is (100 - j100) km/h.

b) Velocity of Q in relation to P:
Velocity of Q - Velocity of P = (200+j500) - (300+j400)

Again, subtracting the real parts and the imaginary parts separately:

Real part: 200 - 300 = -100
Imaginary part: 500 - 400 = 100

Therefore, the velocity of Q in relation to P is (-100 + j100) km/h.

To determine the velocity of P in relation to Q, we need to subtract the velocity of Q from the velocity of P. Similarly, to determine the velocity of Q in relation to P, we need to subtract the velocity of P from the velocity of Q.

a) Velocity of P in relation to Q:
Velocity of P = (300 + j400) km/h
Velocity of Q = (200 + j500) km/h

To find the velocity of P in relation to Q, we subtract the velocity of Q from the velocity of P:

Velocity of P in relation to Q = Velocity of P - Velocity of Q
= (300 + j400) - (200 + j500)

To subtract complex numbers, we subtract the real parts and the imaginary parts separately:

Velocity of P in relation to Q = (300 - 200) + (j400 - j500)
= 100 - j100

Therefore, the velocity of P in relation to Q is (100 - j100) km/h.

b) Velocity of Q in relation to P:
Velocity of P = (300 + j400) km/h
Velocity of Q = (200 + j500) km/h

To find the velocity of Q in relation to P, we subtract the velocity of P from the velocity of Q:

Velocity of Q in relation to P = Velocity of Q - Velocity of P
= (200 + j500) - (300 + j400)

Using the same process as before, we subtract the real parts and the imaginary parts separately:

Velocity of Q in relation to P = (200 - 300) + (j500 - j400)
= -100 + j100

Therefore, the velocity of Q in relation to P is (-100 + j100) km/h.