Express the complex number in trigonometric form. -5i

Answer:[tex]\large\boxed{-5i=5\left(\cos\dfrac{3\pi}{2}+i\sin\dfrac{3\pi}{2}\right)}[/tex]Step-by-step explanation:Look at the picture.The trigonometric form of a complex number:[tex]z=|z|(\cos\alpha+i\sin\alpha)[/tex]where:[tex]|z|=\sqrt{a^2+b^2}\\\\\cos\alpha=\dfrac{a}{|z|}\\\\\sin\alpha=\dfrac{b}{|z|}[/tex]We have the complex number z = - 5i → z = 0 + (-5)i → a = 0, b = -5.Substitute:[tex]|z|=\sqrt{0^2+(-5)^2}=\sqrt{0+25}=\sqrt{25}=5\\\\\cos\theta=\dfrac{0}{5}=0\\\\\sin\theta=\dfrac{-5}{5}=-1[/tex]Therefore[tex]\theta=\dfrac{3\pi}{2}[/tex]Finally:[tex]-5i=5\left(\cos\dfrac{3\pi}{2}+i\sin\dfrac{3\pi}{2}\right)[/tex]