Question

How do you express 1 – 3i in polar form?

Answer 1

`(sqrt10 , - 1.25 )`

Explanation:

Using the formulae that links Cartesian to Polar coordinates.

`• r^2 = x^2 + y^2`

`• theta = tan^-1 (y/x )`

[ 1 - 3i is in 4th quadrant and care must be taken to ensure

that `theta` is in the 4th quadrant ]

(Here x = 1 and y = - 3 )

`r^2 = 1^2 + (-3)^2 = 1 + 9 = 10`

`rArr r = sqrt10`

and `theta = tan^-1 (-3) = - 1.25 color(black)("radians" )`

`theta = - 1.25 color(black)(" is in the 4th quadrant")`