The discussion revolves around finding the polar and Cartesian forms of the complex expression \((-1+i)/(√2)\) raised to the power of 1002. The subject area includes complex numbers, polar coordinates, and exponential forms.
Participants are actively engaging with the problem, questioning each other's calculations and assumptions regarding the argument of the complex number. Some guidance has been offered regarding the correct angle and the need to consider the power in the final expression, but no consensus has been reached on the final form.
There is an ongoing discussion about the correct value of the argument and the implications of raising the complex number to a power, with some participants noting potential errors in earlier calculations.
HallsofIvy said:Your main problem is that [itex]arctan(-1)[/itex] is NOT [itex]5\pi/6[/itex]!
Calculate that again.
NewtonianAlch said:Well, yes (3pi)/4 is the angle you're looking for since this is in the second quadrant.
You have got |z|, and now you have the angle.
Put it into exponential form to the power of 1002, and simplify it to get the angle in terms of a principal argument.
charmedbeauty said:Ok so now I have 1^1002*(cos 3Pi/4+isin3Pi/4)
= 1*(0)=0 how do they get the minus i?
NewtonianAlch said:How did you get 0 for (cos 3Pi/4 + isin 3Pi/4) ?
Also, you have forgotten to raise that to the power.
charmedbeauty said:isnt cos 3pi/4=-0.7...
and sin 3pi/4=0.7...