Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: complex number
Description: in the note describing the imaginary unit, imaginary numbers, the definition of complex numbers, conjugate of complex numbers, and the arithmetic operation of complex numbers
Description: in the note describing the imaginary unit, imaginary numbers, the definition of complex numbers, conjugate of complex numbers, and the arithmetic operation of complex numbers
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Complex number
To understand complex number, first we have to understand imaginary unit
...
The imaginary unit "i" is defined as the square root of -1
...
However, it's used
to extend the number system to include complex numbers
...
For example 2i, 3i ,10i, here number 2,3,and 10 are real number but associated
with’ “I” became imaginary number
...
" Complex numbers are used to represent quantities that involve both
a real part and an imaginary part
...
Real Part (a): The real part of a complex number represents the portion of the
number that lies on the real number line
...
2
...
" It's what gives the
complex number its "imaginary" nature
...
It involves changing the sign of the imaginary part
...
These operations follow certain rules
based on the properties of real and imaginary numbers
...
Addition
Consider complex number Z1 = a1 + b1i
Z2 = a2 + b2i on addition
Z1 + Z2 = ( a1 + b1i ) + (a2 + b2i ) = (a1 + a2 ) + ( b1 + b2 )i
Subtraction
Z1 - Z2 = ( a1 + b1i ) - (a2 + b2i ) = (a1 - a2 ) + ( b1 - b2 )i
Addition
Example:
Subtraction
Example:
Solution
Solution
(2 + 3i) + (4 - 2i)
(2 + 3i) + (4 - 2i) = (2+4) + ( 3 - 2)i
2i = (2-4)+(3+2)i
= 6 + i Ans
...
Solution
Z1* Z2 = (a + bi ) * (c + di ) = a(c + di ) + bi(c + di )
= ac+adi + bci + bd�2 it is evident that �2 = -1
= ac+adi + bci + bd(-1)
= ac+adi + bci - bd = (ac - bd) + ( ad +bc )i → (1)
Z1 = (2 + i) Z2 = (3 - 2i) Simplify Z1* Z2
Solution
Z1* Z2= (2 +i�) * (3 - 2i) = 2*(3 - 2i) + i* (3 - 2i)
= 6 - 4i + 3i - 2�2 = 6 - 4i+ 3i - 2(-1)
= 6 - � + 2 = 8 - � Ans
...
=
��+�̸�−�̸�+�
Title: complex number
Description: in the note describing the imaginary unit, imaginary numbers, the definition of complex numbers, conjugate of complex numbers, and the arithmetic operation of complex numbers
Description: in the note describing the imaginary unit, imaginary numbers, the definition of complex numbers, conjugate of complex numbers, and the arithmetic operation of complex numbers