​ Convert the following into polar form. (2 score each) 1. 1 + i 2. -1 + i 3. √3 – i ​

Question

Convert the following into polar form.

1. 1 + i

2. -1 + i

3. \(\sqrt{3}\) – i

4. \(\frac{5- \sqrt3 i}{4 + 2\sqrt 3 i}\)

Answer 1

1. Given; 1 + i = r(cosθ + isinθ)

r = \(\sqrt{1+1} = \sqrt{2}\)

tanα = \(|\frac{1}{1}|\)= 1 

⇒ α = \(\frac{\pi}{4}\)

The complex number lies in the first quadrant;

2. -1 + i = r(cosθ + isinθ)

r = \(\sqrt{1+1} = \sqrt{2}\)

tanα = \(|\frac{1}{1}|\) = 1 ⇒ α = \(\frac{π}{4}\)

The complex number lies in the second quadrant;

3.

The complex number lies in the fourth quadrant;
 

4.

 The complex number lies in the fourth quadrant;