Holiday homeworkk

[Lighties]

Find a in terms of b. It might help if you think of it in terms of the unit circle. =S

So if b is the angle theta, then what would the angle a be, in terms of theta?

(I haven't looked at the spesh 3/4 course yet, I'm basing this off MM)

[mandy]

Is the answer something like ?

Yes, it is ! How did you get there?

[kamil9876]

This is clear from the unit circle since you can see that rotating a line by 180 degrees doesn't change its gradient.

[cipherpol]

lulz, I'm terrible at explaining.

The period of tan function is .

, where tan b is in first quadrant, tan a is in third.

Since its period is ,if we add , the value of tan will still be the same.

[mandy]

Ok, I think I get it. All this unit circle stuff is really confusing. Thank you cipherpol, Lighties and kamil

[kakar0t]

Hey guys, could you please help me with number 12, i'm not exactly sure what the question is asking me to do


and could you please help me with part c)


Thank you in advance

[kamil9876]

it's asking to basically find the set of all complex numbers such that their squares are in S. So like for instance is such a number since its square is: which satisfies the conditions since the magnitude is and .

Your task for part i.) is to find all such complex numbers.