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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

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Complex number

To understand complex number, first we have to understand imaginary unit
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The imaginary unit "i" is defined as the square root of -1
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However, it's used
to extend the number system to include complex numbers
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For example 2i, 3i ,10i, here number 2,3,and 10 are real number but associated
with’ “I” became imaginary number
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" Complex numbers are used to represent quantities that involve both
a real part and an imaginary part
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Real Part (a): The real part of a complex number represents the portion of the
number that lies on the real number line
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2
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" It's what gives the
complex number its "imaginary" nature
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It involves changing the sign of the imaginary part
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These operations follow certain rules
based on the properties of real and imaginary numbers
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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
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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
...


=

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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