Final answer:
The arctan function can be used to convert between rectangular and polar forms of a complex number. To convert from rectangular to polar form, use the arctan function to find the angle and the Pythagorean theorem to find the magnitude. To convert from polar to rectangular form, use trigonometric functions and the Pythagorean theorem.
Step-by-step explanation:
The arctan function can be used to convert between rectangular and polar forms of a complex number. In the rectangular form, a complex number is represented as a + bi, where a is the real part and b is the imaginary part. In the polar form, a complex number is represented as r(cos(theta) + i sin(theta)), where r is the magnitude of the complex number and theta is the angle it makes with the positive real axis.
To convert from rectangular to polar form, we can use the arctan function. The arctan function takes the ratio of the imaginary part to the real part and returns the angle in radians. We can then use the Pythagorean theorem to find the magnitude of the complex number.
To convert from polar to rectangular form, we can use trigonometric functions such as cosine and sine. We can use the cosine function to find the real part of the complex number and the sine function to find the imaginary part. The magnitude of the complex number can be found using the Pythagorean theorem.