# z1z2

1. ### prove f(z1)=f(z2) implies z1=z2 and maps to D(0;1)- Complex analysis

f(z)={z\over 1+|z|} (i) Prove that f(z_1)=f(z_2) implies z_1=z_2. (iv) Prove that f maps \mathbb{C} onto D(0;1). [The text suggests using polar coordinates for both of these problems.]
2. ### Z_{1}=z_{2}

Suppose z_1=r_1(\cos(\theta_1)+i\sin(\theta_1)) and z_2=r_2(\cos(\theta_2)+i\sin(\theta_2)). If z_1=z_2, then how are r_1 \ \mbox{and} \ r_2 related? How are \theta_1 \ \mbox{and} \ \theta_2 related? If z_1=z_2, then a_1=a_2 \ \mbox{and} \ b_1=b_2. Therefore, r_1=r_2 and \theta_1=\theta_2...
3. ### Find (Z1)(Z2) Leave answer in polar form

Given: Z1= sqrt.6(cos(5pi/6) + i sin(5pi/6)) Z2= sqrt.2(cos(5pi/4) + i sin (5pi/4)) Find (Z1)(Z2) Leave answer in polar form This is what i got so far and i don't know if i started right. =sqrt.12(cos(5pi/6) + i sin(5pie/6)) (cos(5pi/4) + i sin(5pi/4)) =sqrt.12(cos(5pi/4) + cos(5pie/6) i...