Do those three expressions remind you of any standard formulas?cr7einstein said:
cr7einstein said:
BvU said:
BvU said:Same thing. Still I get an imaginary number as sum, zero as a product and one real nonzero term in sum of dyadic products ...
BvU said:So ##\cos{\pi\over 6} + i\sin {\pi\over 6},\ \ 0,\ \ \cos{5\pi\over 6} + i\sin {5\pi\over 6}##.
Sum imaginary, product zero, and sum of dyadic products real, respectively ...
BvU said:So ##\cos{\pi\over 6} + i\sin {\pi\over 6},\ \ 0,\ \ \cos{5\pi\over 6} + i\sin {5\pi\over 6}##.
Sum imaginary, product zero, and sum of dyadic products real, respectively ...
Thanks guys !Nonzero complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a and b are real numbers and i is the imaginary unit equal to the square root of -1. Nonzero complex numbers are different from real numbers, which only contain a real part, and imaginary numbers, which only contain an imaginary part.
Nonzero complex numbers are represented on the complex plane as points with coordinates (a,b), where a is the real part and b is the imaginary part. The horizontal axis represents the real numbers, while the vertical axis represents the imaginary numbers. The origin (0,0) on the complex plane represents the number 0, which is neither real nor imaginary.
The magnitude of a nonzero complex number is its distance from the origin on the complex plane. It is calculated using the Pythagorean theorem, by taking the square root of the sum of the squares of the real and imaginary parts. The magnitude of a nonzero complex number is always a positive real number.
To add or subtract nonzero complex numbers, you simply combine the real parts and the imaginary parts separately. For example, to add (3+2i) and (5-4i), you would add 3 and 5 to get the real part, and add 2i and -4i to get the imaginary part, resulting in (8-2i). This follows the same rules as adding and subtracting polynomials.
The conjugate of a nonzero complex number a + bi is the complex number a - bi. In other words, the conjugate of a nonzero complex number simply changes the sign of the imaginary part. The product of a nonzero complex number and its conjugate always results in a real number, as the imaginary parts cancel out.
