There are six available attributes for any complex number:
Below is a diagram showing the complex number [4, 3]. The attribute values for real, imaginary, magnitude and degrees are labeled for that point.
attribute | formula | value |
---|---|---|
magnitude | sqrt(4 * 4 + 3 * 3) | 5 |
sum_of_squares | 4 * 4 + 3 * 3 | 25 |
The attribute radians measures the angle a point makes with the origin, just like degrees, only the units are different. A good analogy for the relationship between degrees and radians would be the relationship between the fahrenheit and celsius temperature scales (they both measure the same thing but the results are expressed in different units).
The relationship between degrees and radians is based upon this equation:
In actuality, 360 degrees does not equal precisely 6.28 radians - it equals 2 * pi where pi is approximately 3.14159265358979323846.
Here is a diagram showing a number of angles in degrees and their equivalent values in radians:
The formulas for converting between degrees and radians are as follows:
Finally, nearly all the attributes have a long and short form
attribute | short form | examples |
---|---|---|
real | real | real(z), real([1, 2]) |
imaginary | imag | imaginary(z), imag([2, 3]) |
magnitude | mag | magnitude(z), mag([3, 4]) |
sum_of_squares | ssq | sum_of_squares(z), ssq([4, 5]) |
degrees | deg | degrees(z), deg([5, 6]) |
radians | rad | radians(z), rad([6, 7]) |