1.1. Note: You may assume throughout this question that $i=\sqrt{-1}$ behaves exactly the same as any other constant for purposes of algebraic manipulation, differentiation and integration.

For a complex number $z=cos \theta +isin \theta$,  where  $\theta \inℝ$,  show that

$\frac{dz}{d \theta }=iz$

1.2. Utilising your knowledge of differential equations, explain briefly why the result of part (a) supports the validity of Euler’s relation

${e}^{i \theta }=cos \theta +isin \theta$