What is the polar form of #(16,4#?
The quickest method is to use the formula:
Below is an alternative method.
Squaring both equations:
Adding both equations:
We only need the positive root, negative radii can exist, and a point can be represented by many different polar coordinates, unlike Cartesian coordinates which are unique.
Polar coordinate:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the polar form of the complex number (16  4i), where (i) is the imaginary unit, follow these steps:

Convert the rectangular form to polar form using the formulas: [ r = \sqrt{x^2 + y^2} ] [ \theta = \arctan\left(\frac{y}{x}\right) ]

Substitute the given values (x = 16) and (y = 4) into the formulas.

Calculate (r) and (\theta).

Write the polar form as (r(\cos(\theta) + i \sin(\theta))).
Let's calculate:
[ r = \sqrt{16^2 + (4)^2} = \sqrt{256 + 16} = \sqrt{272} = 4\sqrt{17} ]
[ \theta = \arctan\left(\frac{4}{16}\right) = \arctan\left(\frac{1}{4}\right) ]
Using a calculator, we find ( \theta \approx 0.24498 ) radians.
So, the polar form of (16  4i) is ( 4\sqrt{17} \left( \cos(0.24498) + i \sin(0.24498) \right) ).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 What is the Cartesian form of #(66,(31pi)/16))#?
 What is the Cartesian form of #(18,(34pi)/8)#?
 How do you evaluate the integral #sin(x^2+y^2)dr# where r is the region #9<= x^2 + y^2 <= 64# in polar form?
 What is the Cartesian form of #(1,(pi )/4)#?
 How do you find the rectangular coordinates of the point with polar coordinates #(1,pi/3)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7