Unit circle Definition and 103 Threads

Can anyone help me with this: Let w be a complex number with the property w \leq 2. Prove that w can be written as a sum of to complex numbers on the unit circle. That is; prove that w can be written as w = z_1 + z_2, where |z_1| = 1 and |z_2| = 1. I really can't come up with a...

In a unit circle, where t is a real number, why is that the following is true: sin (t+2pi)=sin t I really don't understand this, if I put any value into t and check on my calculator, sint and sin(t+2pi) give different answer, why is this? Thanks for any help

How do I derive the formula 'Sin(a+b)=sinacosb + cosasinb' from the unit circle. Any ideas would be appreaciated our study group tried and failed.