Question

Convert the complex number z = 4 - 10i from rectangular form to polar form.​

Answer 1

`r = 2 √(29) ( \cos(292 \degree) + \sin(292 \degree))`

Step-by-step explanation

The polar form of a complex number ,

`z = x + yi`

is given by:

`z = r( \cos( \theta) + i \sin( \theta) )`

where

`r = \sqrt{ {x}^(2) + {y}^(2) }`

The given complex number is:

`z = 4 - 10i`

`r = \sqrt{ {4}^(2) + {( - 10)}^(2) }`

`r = √(16 + 100)`

`r = √(116) = 2 √(29)`

And

`\theta= \tan^( - 1)(( y)/(x) )`

`\theta= \tan^( - 1)(( - 10)/(4) )`

`\theta= 292 \degree`

Hence the polar form is :

`r = 2 √(29) ( \cos(292 \degree) + \sin(292 \degree))`