FactChecker said:The sin of both those angles are the same, so you must decide which is correct. That is the angle that has the correct a,b values. 52 degrees would be at (3.18, 4.19) and 127.2 degrees is at (-3.18, 4.19).
The polar form of a complex number is a way of representing a complex number in terms of its magnitude (or modulus) and its argument (or angle). It is expressed in the form r(cosθ + isinθ), where r is the modulus and θ is the argument.
To convert a complex number to polar form, you can use the formula r = √(a² + b²) to find the modulus, where a and b are the real and imaginary parts of the complex number, respectively. Then, you can use the formula θ = tan⁻¹(b/a) to find the argument. Finally, the polar form can be written as r(cosθ + isinθ).
The main difference between polar form and rectangular form is the way they represent a complex number. Rectangular form is expressed in the form a + bi, where a and b are real numbers, while polar form is expressed in the form r(cosθ + isinθ), where r is the modulus and θ is the argument.
To graph a complex number in polar form, you can use the modulus and argument to determine the coordinates of the point on the complex plane. The modulus represents the distance from the origin, and the argument represents the angle from the positive real axis in a counterclockwise direction. You can then plot the point on the complex plane.
One advantage of using polar form for complex numbers is that it provides a geometric interpretation of the number. The modulus gives the magnitude of the number, while the argument gives the direction. This can be useful in understanding the properties of complex numbers and their operations. Additionally, polar form can also make calculations involving complex numbers easier, especially when dealing with powers and roots.