BodhiAI
Nov. 11, 2019

#### Power of iota & standard form of complex number:

Complex Numbers

A complex number may be defined as an ordered pair of real numbers and may be denoted by the symbol (a, b). If we write z = (a, b), then a is called the real part and b is called the imaginary part of z and may be denoted by Re(z) and Im(z) respectively.

Leonhard Euler was the first mathematician to introduce the greek symbol (read as iota) in or around 1977.

Mathematically, is equal to square root of -1, such that = -1. He also called this symbol as imaginary unit.

Equality of Complex Numbers

Two Complex Numbers are said to be equal if their Real parts and Imaginary Parts separately are Equal.

i.e.

a = c and b = d

Property of Order

Complex Number does not posses Property of Order i.e. We cannot compare two complex numbers apart from equality.

is NOT DEFINED

Example: Which of the following is correct?

(A) 1+ > 2- (B) 2 + > 1+

(C) 2- > 1+ (D) None of these

Since, the complex numbers do not posses properly of order.

The operations > or < are not defined in case of complex numbers.

Hence, the correct answer is (D)

Integral Powers of IOTA

(i) (v)

(ii) (vi)

(iii) (vii)

(iv) (viii)

In General

(a) (d)

(b) (e)

(c)