Question

How to find path of a complex no as a function of t?

Answer 1

$\mathfrak{The\:Answer\:is}$


Let 1−i→a−i→a+4i→−2+4i1−i→a−i→a+4i→−2+4iand find a∈Ra∈R.

(2)

Probably you mean Figure Eight Curve

(3)

z=e2πit+1z=e2πit+1 is the circle |z−1|=1|z−1|=1or z=1+cos2πt+isin2πtz=1+cos⁡2πt+isin⁡2πt where 0≤t≤10≤t≤1. In this case with 1−t1−t the path traced in apposite direction and the factor t3t3 instead of tt caused the path spanned 3 times faster. So desired path is z=1+cos2π(1−t3)+isin2π(1−t3)z=1+cos⁡2π(1−t3)+isin⁡2π(1−t3) where 0≤t≤30≤t≤3.




$\boxed{Hope\:This\:Helps}$