In this way we can also think of a complex number as an ordered pair of real numbers, z=(x,y). We can think of x as being the real part of the complex number, z. In Mathematica we can find the complex conjugate of an expression by using the command Conjugate.Д®xercise CN-3: When is a complex number equal to its complex conjugate?Д®xercise CN-4: How do complex numbers come into play with quadratic equations? When we replace i by - i, we have the complex conjugate of z, and we write this. One way of defining a complex number, z, is to say it is the sum of a real number, say x, and an imaginary number, say i y, In engineering, the imaginary unit is often given the symbol j.Д®xercise CN-2: What are the first four powers of i? The symbol i is what we call the imaginary unit and any product of a real number with the imaginary unit is called an imaginary number. What happens if the square is a negative, number? We cleverly choose the symbol i to represent this case, Thus, when we take the root of a positive number, the answer must almost always be in the form of a pair, a positive number and a negative number. It matters not that the base is negative. When we take the square of a number, the answer is always positive. Complex numbers are vital to performing many calculations in physics.

Mathematica complex conjugate