Complex numbers and examples to understand
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is an imaginary unit that satisfies the equation i^2 = -1. Complex numbers extend the real number system by introducing the imaginary unit.
Here are a few examples of complex numbers:
1. 3 + 2i: This is a complex number where the real part is 3 and the imaginary part is 2.
2. -5i: This is a complex number where the real part is 0 and the imaginary part is -5.
3. 1 - i: This is a complex number where the real part is 1 and the imaginary part is -1.
4. 4: This may seem like a real number, but it can also be considered a complex number with the imaginary part being 0.
Complex numbers can be added, subtracted, multiplied, and divided just like real numbers. For example, let's perform some operations with complex numbers:
Addition: (3 + 2i) + (1 - i) = 4 + i
Subtraction: (3 + 2i) - (1 - i) = 2 + 3i
Multiplication: (3 + 2i) * (1 - i) = 5 + i
Division: (3 + 2i) / (1 - i) = (1/2) + (5/2)i
Complex numbers can also be plotted on a complex plane, where the real part is represented on the x-axis and the imaginary part is represented on the y-axis. This allows for visualizing and understanding the properties of complex numbers.