Question

Which has the lesser value, -5 or -5i?

Answer 1

They have exactly the same magnitudal value, as |-5|=|-5i|

Answer 2

(The magnitude of a complex \(|z|=z\cdot z^*=(\Re(z)+i\Im(z))(\Re(z)-\Im(z)) \) so, yeh)

Answer 3

Oops, \(-i\Im(z)\) for that last part

Answer 4

So, you're saying -5 is the same as -5(√-1) I'm sorry but I don't get what you just typed there.

Answer 5

The numbers are the same size, but not the same value.

Answer 6

All right, here, \(\Re(z)\) is the "real part of z" (where \(z=a+bi\) ), which could be seen as \(a\), and \(\Im(z)\) is the "imaginary part of z" which would be \(b\) in this case. You cannot define a notion of greater than or less than, other than by defining each part of the number to be larger than some value, or for its magnitude to be larger than some value.

Answer 7

(I am, of course, referring to complex numbers, in this case)

Answer 8

Okay, I kinda get it know. But I'm still confused to some degree because I got this question for homework: What are the roots of the polynomial equation:(x + 5)(x + 5i)(x - 5i) = 0 Enter your answers in order from least to greatest, separated by a comma.
The thing is I don't know which one should I put first, -5 or -5i.

Answer 9

Oh, haha, er... I... don't really know, actually. If you get it wrong ask your teacher, or something of the like (preferable if you can it before?)... frankly, that's so specific that, well, I have no clue what to answer, in this case.

Answer 10

Yea, I should probably contact the teacher. I'm taking the class online so if I get the answer wrong I only have another attempt to try it again. I just don't wanna risk it. Thanks though. You're a great help.

Answer 11

Sure thing