10.3.10 Operations with complex numbers

Problem: A complex number is given: \( z=\frac{-4 \sqrt{3}-4 i}{1+i \sqrt{3}} \). 1) Write the complex number in algebraic, trigonometric and exponential forms. 2) Write the algebraic, trigonometric and exponential forms of the number \( u=z^{n} \), where \( n(-1)^{N}(N+4), N=25 \). 3) Write the exponential and trigonometric forms of the roots \( W_{k}=\sqrt[3]{z}, k=0,1,2 \). 4) Draw \( z \) and \( W_{0}, W_{1}, W_{2} \) on the same complex plane.