complex numbers form the basis of a significant number of calculations in maths..lets learn something about them..now,lets try to find out square roots of some numbers..what is the answer of square root of 1 and 4?its obviously 1 and 2..now,try finding the square root of a number not to the right but to the left of zero in the number line...perplexed?can't find the square roots of -1,-4 etc..here's where complex numbers come in...the solutions which u get by solving the quadratic equation x^2+x+1=0 are called the cube roots of unity..each cube root of unity is square of the other...a complex number is represented as x+iy where x is the real part and iy is the imaginary part..i is the square root of -1 and is called iota..

some of the properties of i are:-

1. i^2n=1 when n is even integer

2.i^2n= -1 when n is odd integer

3.i^2n+1= i when n is an even integer

4.i^2n+1= -i when n is an odd integer

reciprocal of a COMPLEX NUMBER:-

if z=x+iy,then its reciprocal 1/z is given by (x/x^2+y^2 - i y/x^2+y^2)

 

modulus of a COMPLEX NUMBER:-

if z =x+iy then mod z =x^2+y^2

next abt complex numbers coming up shortly..