Divide the magnitudes and subtract the angles.pat666 said:Homework Statement
(5∠2.214)/(√5∠-1.107)
ive gotten this far in a problem(thats the answer but i need to simplify).. all i need to know is how to divide the angles?
Homework Equations
The Attempt at a Solution
"Divide Polar Form" refers to the process of dividing two complex numbers expressed in their polar form, which consists of a magnitude (represented by the number before the angle symbol) and an angle (represented by the number after the angle symbol).
The number before the angle symbol (2.214) represents the magnitude or distance from the origin of the complex number, while the number after the angle symbol (-1.107) represents the angle or direction of the complex number in radians. The square root symbol (√) indicates that the number following it is the square root of the number before it.
To divide two complex numbers in polar form, you must first convert them into rectangular form, then perform the division using the formula (a+bi)/(c+di) = [(ac+bd)/(c^2+d^2)] + [(bc-ad)/(c^2+d^2)]i. After obtaining the result in rectangular form, you can convert it back to polar form by using the formula r = √(a^2+b^2) and θ = tan^-1 (b/a).
The result of dividing 5∠2.214 by √5∠-1.107 is approximately 3.162∠3.321.
The division of complex numbers in polar form can be useful in analyzing alternating currents in electrical engineering, modeling wave propagation in physics, and solving problems in navigation and surveying that involve direction and distance.