Mathematics, 11.10.2019 22:50 MZ2017
Write the complex number in the form a + bi. 4[cos (-135°) + i sin (-135°)]
Answers: 2
![\bf \begin{array}{llll} 4[cos(&-135^o)+i\ sin(&-135^o)]\\ \uparrow &\quad \uparrow &\quad \uparrow \\ r&\quad \theta&\quad \theta \end{array}\qquad \begin{cases} x=rcos(\theta)\\ y=rsin(\theta)\\ ----------\\ r=4\\ \theta=-135^o\\ cos(-135^o)=-\frac{\sqrt{2}}{2}\\ sin(-135^o)=-\frac{\sqrt{2}}{2}\\ \end{cases} \\\\\\ x=4\left( -\frac{\sqrt{2}}{2} \right)\implies x=-2\sqrt{2} \\\\\\ y=4\left( -\frac{\sqrt{2}}{2} \right)\implies y=-2\sqrt{2}\\\\ -----------------------------\\\\](/tpl/images/0311/5394/4255b.png)
![Write the complex number in the form a + bi. 4[cos (-135°) + i sin (-135°)]](/tpl/images/0311/5394/d9827.jpg)
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