Hi, I have recently been set a set of questions all of which I have been able to do apart from the last part, I just need a starting point if at all possible or some guidance. The question is as follows:

given the 2D trajectory:

r(t) = vector (x(t) y(t))

= vector (a*cos(omega*t) b*sin(omega*t))

show that r(t) can be expressed as:

r(t)=Re(Re^(i*omega*t)) where Re is the real part andRis the complex amplitude vector (X Y)

The hint is Re(z)=(z + z*)/2 to deduce what X and Y are in terms of a and b.

Ive already plotted the data and deduced that it can be expressed as:

x^2/a^2+y^2/b^2=1

Ive tried different things including working backwards and converting e^(i*omega*t) into the real and imaginary parts (a*cos(omega*t) + i*b*sin(omega*t) etc.) but to no avail. Any help would be much appreciated.