Question

express it in a vomplex number in the form of r(cos theta + i sin theta)​

Answer 1

Answer:

$\frac{1 - i}{cos \frac{ \pi}{3} + i \: sin \frac{ \pi}{3} } \\ = \frac{1 - i}{cos \: 60 \degree + i \: sin 60 \degree } \\ = \frac{1 - i}{ \frac{1}{2} - \frac{ \sqrt{3} }{2} } \\ = \frac{1 - i}{ \frac{1 - \sqrt{3} }{2} } = \frac{2(1 - i)}{1 - \sqrt{3} } \\ = \frac{2(1 - i)}{1 - \sqrt{3} } \times \frac{(1 + \sqrt{3} )}{(1 + \sqrt{3} )} \\ = \frac{2(1 - i) \times(1 + \sqrt{3} ) }{(1 - \sqrt{3}) \times (1 + \sqrt{3} )} \\ = 2 \times \frac{1(1 + \sqrt{3}) - i(1 + \sqrt{3}) }{ {1}^{2} - {( \sqrt{3}) }^{2} } \\ = 2 \times \frac{1 + \sqrt{3} - i - i \sqrt{3} }{ 1 - 3} \\ = 2 \times \frac{1 + \sqrt{3} - i - i \sqrt{3} }{ - 2} \\ = \frac{1 + \sqrt{3} - i - i \sqrt{3} }{ - 1} \\ = - (1 + \sqrt{3} - i - i \sqrt{3} ) \\ = - (1 + \sqrt{3} ) + i(1 + \sqrt{3} )$

Answer 2

Answer:

Step-by-step explanation:

This can be summarized as follows: The polar form of a complex number z=a+bi is z=r(cosθ+isinθ) , where r=|z|=√a2+b2 , a=rcosθ and b=rsinθ , and θ=tan−1(ba) for a>0 and θ=tan−1(ba)+π or θ=tan−1(ba)+180° for a<0 . Example: Express the complex number in polar form.