Question

Express –1–i in polar form with principle value of the amplitude

Answer 1

Answer:

$z= \sqrt{2} ( \cos( \frac{3\pi}{4} ) - i \sin( \frac{3\pi}{4} ) ).$

Step-by-step explanation:

$z = - 1 - i \\ \\ |z| = \sqrt{ {1}^{2} + {1}^{2} } = \sqrt{2} \\ \\ \alpha = \frac{\pi}{4} - \pi \\ \\ = - \frac{3\pi}{4} \\ \\ therefore \: \: \: \: \: z = \sqrt{2} ( \cos( - \frac{3\pi}{4} ) + i \sin( \frac{ - 3\pi}{4} ) ) \\ \\ \\ \\ z= \sqrt{2} ( \cos( \frac{3\pi}{4} ) - i \sin( \frac{3\pi}{4} ) ).$