Complex arithmetic is a branch of mathematics that deals with operations and properties of complex numbers. It involves addition, subtraction, multiplication, and division of complex numbers, as well as other operations such as conjugation and powers.
To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, (3+2i) + (1+4i) = (3+1) + (2i+4i) = 4 + 6i. The same process applies for subtraction.
Yes, complex numbers can be multiplied and divided using the same rules as for real numbers. To multiply, you distribute and combine like terms. For division, you use the conjugate of the denominator to eliminate the imaginary part in the denominator.
Complex numbers can be graphed on a complex plane, where the real part is represented on the horizontal axis and the imaginary part is represented on the vertical axis. The location of the complex number on the plane corresponds to its value.
Complex arithmetic is used in many fields such as physics, engineering, and economics. Some examples of its applications include analyzing electrical circuits, modeling vibrations in mechanical systems, and predicting stock market trends. It is also used in signal processing and control systems.