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anonymous
 3 years ago
explain why j2 = 1 and not 1?
anonymous
 3 years ago
explain why j2 = 1 and not 1?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i believe the definition comes from the complex variable plane, where Im is the y axis and x is Re, then magnitude of a unit vector along 1 on Im axis is defined as sqrt(1) I'm not sure if that's correct though, look up complex plane

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Is it *i* in place of *j*??? @ketz ... It should be... 'i' is the positive square root of 1...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes j instead of i...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1362154909600:dw

whpalmer4
 3 years ago
Best ResponseYou've already chosen the best response.0Electrical engineers typically use \(j^2 = 1\) instead of \(i^2 = 1\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's just the definition.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0That's how it is defined. j^2 = 1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0a complex number is represented as \[z=x+iy\] where x is the real part and y is the imaginary part. all real numbers R are a subset of complex numbers C, for example number 3 has x=3 and y=0 so that only the real part is left. the definition of i (or j) = sqrt(1) comes from multiplication rule for complex numbers. \[z_1*z_2=(x_1,y_1)(x_2,y_2)=(x_1x_2  y_1y_2,x_1y_2+x_2y_1)\] if z1=(0,1) and z2=(0,1), that is they both only contain imaginary parts, then \[i^2=(0,1)(0,1)=(1,0)=1\] as you can see that after multiplying them out following the formula above we are left with a real part that equals to 1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0as a side note, the reason electrical engineers use j instead of i is because they use i to represent current
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