Question

um número complexo z tem módulo raiz 2 e argumento 135°. Qual a sua forma trigronométrica e algébrica?​

Answer 1

$\Large\boxed{\begin{array}{l}\sf \rho=\sqrt{2}~\theta=135^\circ\\\sf z=\rho\cdot[cos(\theta)+i~sen(\theta)]\\\boxed{\boxed{\boxed{\boxed{\sf z=\sqrt{2}[cos(135^\circ)+i~sen(135^\circ)]}}}}\\\\\sf z=\sqrt{2}\bigg[-\dfrac{\sqrt{2}}{2}+i~\dfrac{\sqrt{2}}{2}\bigg]\\\\\sf z=-\dfrac{2}{2}+\dfrac{2}{2}i\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf z=-1+i}}}}\end{array}}$