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ketz

  • 2 years ago

explain why j2 = -1 and not 1?

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  1. arjont
    • 2 years ago
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    i 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

  2. saloniiigupta95
    • 2 years ago
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    Is it *i* in place of *j*??? @ketz ... It should be... 'i' is the positive square root of -1...

  3. ketz
    • 2 years ago
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    yes j instead of i...

  4. saloniiigupta95
    • 2 years ago
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    |dw:1362154909600:dw|

  5. whpalmer4
    • 2 years ago
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    Electrical engineers typically use \(j^2 = -1\) instead of \(i^2 = -1\)

  6. wio
    • 2 years ago
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    It's just the definition.

  7. Xavier
    • 2 years ago
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    That's how it is defined. j^2 = -1

  8. arjont
    • 2 years ago
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    a 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

  9. arjont
    • 2 years ago
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    as a side note, the reason electrical engineers use j instead of i is because they use i to represent current

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