Maths complex number class11




What is COMPLEX NUMBER?

A number in the form a + i b, where a and b are real numbers and i denotes the imaginary unit.For example √-1,√-2 etc. are imaginary numbers We denote √-1 by the Greek letter ‘i’, called iota and in complex number imaginary number play an important role.
complex number

i  = √-1 ,
i2   = -1,
i3  = i. i= -i,
i4  = i2     i2   = (-1) (-1) = 1

Imaginary number i value of i5 ,i6 ,i7 ,i8 till in term all will be expressed in same value like i or -1 or –i or 1.

Example  i7will be written i. i=1.-i = -i 

Now if i17 we can’t do same every time so there is a TRICK. We divide the power of imaginary number by ‘4’.

SO FOLLOW THE STEPS HOW TO SOLVE.

# First Step
i17 you have seen imaginary power is 17 divide it by 4 it will give remainder 1.

# Second Step
Now the 1 you got will be the power of you imaginary number i1 and that will be your answer.

CONCLUSION – If the imaginary power is more than 4 you have to just divide it by 4 and the remainder your new imaginary power and it will be your answer.
Example  i39 on dividing by 4 we get remainder 3  i3 = -i.

# HOW TO FROM COMPLEX NUMBER
We represent Complex Number ‘Z’ and if we write Z=a+ib. so this is called a complex number.
Were a and b both are Real.
A is called real part of complex number and we represent it by Re(Z).
B is called imaginary part of complex number and we represent it by Img(Z).So any number is a complex number.

Example Z = 5 So we can write 5 by = 5 + i0 
 Here Re(5) and Img(0)
Any number we can write in form of complex number.
# PRPORTY OF A COMPLEX NUMBER

* How to add two complex number 

Suppose z1=a1+ib1 and z2=a2+ib2  
When we add
z1+ z2 = (a1+ib1) + (a2+ib2)
Note- Real part will add to real part and imaginary part with imaginary part.
(a1+a2) + i(b1+b2)
Now if we have to add three or more complex number Z3=a3+ib3
z1+ z2+z3 = (a1+a2+a3) + i(b1+b2+b3)  and same till nth term.           
Example: (3 + 2i) + (1 + 7i) = (4 + 9i)

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