There are three very common ways of writing any complex number z: Standard form: z = x + i y Polar form: z = |z| (cosφ + i sinφ) Exponential form: z = |z| eiφ In this post we explain how to get from any of these representations to the other ones. From standard formContinue reading “How to convert a complex number to polar form and back”
Category Archives: basics
What is a cartesian product?
The cartesian product M1×M2 of two sets M1 and M2 is the set of all pairs (x1,x2) with x1∈M1 and x2∈M2. More generally, the cartesian product M1×M2×…×Mn of n sets M1,M2, …,Mn ist the set of all n-tuples (x1,x2,…,xn) with x1∈M1, x2∈M2, …, xn∈Mn. We may write Before we turn to some examples, let usContinue reading “What is a cartesian product?”
How to prove by induction
Mathematical induction is a method to systematically prove that a statement which depends on an integer is true for all values of this integer which are greater than some number. Let us be more precise and call S(n) a statement which involves an integer n (not to be confused with a function of n). AnContinue reading “How to prove by induction”
How to divide by a complex number
When we divide a complex number by another one, say we usually want to obtain the result in standard form. So how do we simplify a quotient such that the result takes the form ? The answer is: We multiply the numerator and the denominator of the quotient by the complex conjugate of theContinue reading “How to divide by a complex number”
math for physicists 