Polar form is a way of representing complex numbers using their distance from the origin (also known as the magnitude or modulus) and the angle they make with the positive real axis (also known as the argument or phase). Rectangular form, on the other hand, represents complex numbers using their real and imaginary parts.
To convert from polar to rectangular form, you can use the following formulas:
Real part (x) = magnitude * cos(argument)
Imaginary part (y) = magnitude * sin(argument)
The resulting complex number will be in the form x + yi.
Converting from polar to rectangular form allows for easier manipulation and calculation of complex numbers. It also allows for a better understanding of the geometric properties of complex numbers.
Yes, you can convert a negative angle to rectangular form. The angle will be measured counterclockwise from the positive real axis, regardless of whether it is positive or negative.
To calculate the modulus of a complex number in rectangular form, you can use the Pythagorean theorem: modulus = sqrt(x^2 + y^2), where x is the real part and y is the imaginary part. To calculate the argument, you can use the inverse tangent function: argument = arctan(y/x), where x and y are the real and imaginary parts, respectively.