Question

Convert the complex number 3 - 3i into its polar representation. a. 3(cos(60degrees) + isin(60degrees)) b. 3√2(cos(135degrees) + isin(135degrees)) c. √3(cos(225degrees) + isin(225degrees)) d. 3√(cos(315degrees) + isin(315degrees))

Answer 1

Answer:

The correct option is B. 3√2(cos(135°) + i·sin(135°))

Step-by-step explanation:

The complex number is given as : 3 - 3i

Now, comparing this with the standard for : a + bi

⇒ a = 3 and b = -3

Now, r = √a² + b²

⇒ r = √18

⇒ r = 3√2

$\tan\theta=\frac{b}{a}\\\\\implies\tan\theta=\frac{-3}{3}\\\\ \implies\tan\theta =-1\\\\ \implies\theta=\frac{3\pi}{4}\\\\\implies\theta=135$

Now, The polar form is represented by :

z = r(cosθ + i·sinθ)

⇒ z = 3√2(cos 135° + i·sin 135°)

Therefore, the correct option is B. 3√2(cos(135°) + i·sin(135°))