Final question of my assigment, can anyone help me so I can celebrate!!
I'm struggling on the following question:
Power in an electric circuit is given by: p = iv
Calculate the maximum value of power if:
v = 0.002Sin (100piet)volts
i = 0.6Sin (100piet + pie/4)amps

and calculate the first time the power reaches a maximum value??

I've had a go at calculating maximum power and got the following:

0.6Sin(100piet + pie/4) x 0.02Sin(100piet)
= 0.012Sin(100piet) - Sin(100piet + pie/4)
= 1/2 x 0.012(cos(100piet -(100piet + pie/4))-cos(100piet+(100piet+pie/4))
= 0.006(cos pie/4 - cos(200piet + pie/4)
as smallest possible value is -1 for cos(200piet +pie/4)
: max value of p = 0.006(cos pie/4 +1)
= 0.0102?
Does this make any sense?

For the second part of the question: First time it reaches maximum power, I need some guidance on this one, I'm not sure where to go with this one?

All help would be greatly appreciated.

2. as far as i concerned, when multiplying complex number you need to multiply the magnitud and add the phase:

now you need to transfrom time-domain to phasor-domain

$v(t)=v_{m}\sin(\omega+\emptyset)\Longleftrightarro w v=v_{m}\angle\emptyset-90^\circ$

$i(t)=i_{m}\sin(\omega+\emptyset)\Longleftrightarro w i=i_{m}\angle\emptyset-90^\circ$

$v=0.002\angle-90^\circ,i=0.6\angle-45^\circ$

$p=vi=0.002\times0.6\angle-45^\circ-90^\circ=1.2\angle-135^\circ mW$