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anonymous
 5 years ago
can u teach me, how i can solve this problem...
Triangle inequality for complex numbers is Z1 + Z2<= Z1 + Z2 . Write down at least eight different conditions for which Z1 + Z2= Z1 + Z2 .
anonymous
 5 years ago
can u teach me, how i can solve this problem... Triangle inequality for complex numbers is Z1 + Z2<= Z1 + Z2 . Write down at least eight different conditions for which Z1 + Z2= Z1 + Z2 .

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let the angle between the two complex position be @ So the length of the Z1+Z2 complex point or in other words Z1+Z2 is = \[\sqrt(Z _{1}^2\sin^2@+Z _{2}^2+Z _{1}^2\cos^2@+Z _{1}Z _{2}\cos@)\] Continued ........................

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let name that expression as A

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now when Z1+Z2=Z1+Z2 Z1+Z2=A

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Squaring both sides and simplifying we get @=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So you can get the equation only when the amplitude of the complex number is the same. I hope you have understood Please note that here the symbol Z1 and Z2 is the magnitude of the actual Z1 and Z2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i got what u had explained...thank you so much...this open stdy really halp me to think out of the box..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0As you asked on through chat how to calculate amplitude of a complex number, so here is the reply Lets take a complex number x+iy So its amplitude is y/x Lets take another example z=3+7i So its amplitude would be 7/3 According the reply I gave you, the equation z1+z2=z1+z2 is valid only when the amplitude of two complex number is the same. So for an example The complex number z1= 2+i4 and the complex number z2=6+i12 holds the relationship z1+z2=z1+z2 Hope, I have made myself clear

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So silly of me! All this time, I have been mentioning a wrong term. I am extremely sorry for that. Please note that in the above answer everywhere I have used the word ""amplitude"", it must be instead ""argument""
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