## Complex Numbers-

Complex numbers come into existence when the square of a number is negative because we know it very well that the square of a number will always be positive doesn’t matter whether the number is positive or negative.

In cases like   or   here, if we solve, we find the square of x=-1. We say that x is not real here. Generally, these types of cases are considered as Complex numbers. Complex numbers were first observed by mathematician Girolamo Cardano (1501-1575). In his book Ars Magna, he discussed the mechanics of complex numbers in details and thus he started Complex Algebra.

### Standard form of Complex Numbers-

Complex numbers are defined as expressions of the form a + ib where a,b R & i =

It is denoted by Z  i.e. z= a + ib.

‘a’  is called as real part of z= (Re z)

and ‘b’ is called as imaginary part of z =(Im z).

i or IOTA- iota is a unique symbol. it’s the ninth letter of Latin alphabet. It’s used to denote imaginary numbers whose square root is -1.

## IB Mathematics HL SL-Maxima and Minima

In my previous post, we discussed how to find the equation of tangents and normal to a curve. There are a few more  Applications of Derivatives in IB Mathematics HL SL, ‘Maxima and Minima’ is one of them.

Maxima and Minima:-

1. A function f(x) is said to have a maximum at x = a if f(a) is greater than every other value assumed by f(x) in the immediate neighbourhood of x = a. Symbolically

gives maxima for a sufficiently small positive h.

Similarly, a function f(x) is said to have a minimum value at x = b if f(b) is least than every other value assumed by f(x) in the immediate neighbourhood at x = b. Symbolically

If x = b gives minima for a sufficiently small positive h.