Question

Determine the polar form of the complex number 5 – 3i. Express the angle θ in degrees, where, 0≤∅≤360° and round numerical entries in the answer to two decimal places.

Question options:

5.83(cos329.04° – isin329.04°)

329.04(cos329.04° – isin329.04°)

329.04(cos5.83 + isin5.83°)

5.83(cos329.04° + isin329.04°)

Answer 1

5.83(cos329.04° + isin329.04°)

Step-by-step expl

Answer 2

Option 4 -> 5.83 ( cos329.04 + i sin 329.04)

Explanation:

Step 1 :

Given complex number is 5 - 3i

Step 2 :

To determine the polar form of the complex number x + iy we need to find r =
`\sqrt{x^(2) + y^(2) }` and angle theta = inverse tan(y/x)

Then the polar form would be r(cos theta + i sin theta)

Step 3 :

so for the given complex number we have r =
`\sqrt{5^(2) + (-3)^(2) } = √(25+ 9) = 5.83`

and theta = inverse tan( 3/5) = 30.96

Here the number is in the 4th quadrant so we have

theta = 360 - 30.96 = 329.04 degrees

Step 4 :

So the required polar form is

5.83 ( cos329.04 + i sin 329.04)

Hence option 4 is the correct answer