Complex Analysis Notes
The area of Mathematics in which we study complex numbers, complex functions complex roots, etc. is called complex numbers.
✅Complex Numbers
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| complex number |
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| complex number example |
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| sperate the real and imaginary part |
Arithmetic operations on complex numbers:
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| addition operation on complex number |
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| subtraction operation on complex number |
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| multiplication operation on complex number |
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| division operation on complex number |
Properties of complex numbers:
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| Properties of complex numbers, commutative, associative, distributive, closure |
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| zero and unity |
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| inverses |
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| reciprocal |
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| conjugate |
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| conjugate property |
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| conjugate property |
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| conjugate property |
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| conjugate property |
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| conjugate property |
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| sum & product of complex number with it conjugate is a real number |
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| sum and product of complex number with its conjugate is real |
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| complex plane |
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| modulus |
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| example of modulus |
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| modulus properties |
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| equation of circle |
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| equation of circle |
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| find the center and radius |
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| solution center and radius finding |
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| center, radius |
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| find a semi-major and minor ellipses |
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| finding semi-major and minor |
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| important point |
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| distance |
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| graphical representation of the above example |
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| when x changes continuously |
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| inequalities |
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| inequalities part 2 |
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| the polar form of a complex number |
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| graphical representation |
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| example of polar form |
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| example of polar form |
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| example of polar form |
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| the argument of the product of complex numbers is equal to the sum of their arguments |
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| product of complex numbers is equal to the sum of their arguments |
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| proof of arguments of the quotient of two numbers is equal to the difference of their arguments |
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| principal arguments |
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| uses theorem of arguments |
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| de-movie's formula |
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| method of finding principal arguments |
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