# If it is never a complex number, then why no solutions?

#1

They say |z| is never a complex number so no possible solutions but what I don't get is how they quickly jump to this conclusion? Could somebody please help
0
3 years ago
#2
(Original post by Kalabamboo)

They say |z| is never a complex number so no possible solutions but what I don't get is how they quickly jump to this conclusion? Could somebody please help
because |z| is real z + 2i must be real so imaginary part of z must be -2i. so if you say z = a-2i then the equation says |z|=a-2i+2i=a which isn't true because |z|=sqrt(a^2+4)

i'm not sure if there is a really quick simpler way to see it though
1
3 years ago
#3
(Original post by Kalabamboo)

They say |z| is never a complex number so no possible solutions but what I don't get is how they quickly jump to this conclusion? Could somebody please help
|z| is the size of modulus of the complex number....the magnitude of the complex number on the argand diagram therefore |z| will only be a number which can never be complex
0
3 years ago
#4
(Original post by Kalabamboo)

They say |z| is never a complex number so no possible solutions but what I don't get is how they quickly jump to this conclusion? Could somebody please help
The modulus of z is the distance of the point z from the origin (pythagoras) so it is always a real number. In order for z +2i to be real, z = x - 2i. However then z +2i will be x and mod(z) will be (x^2 + 2^2)^0.5 which is always larger than x so they can't equal each other. I'm not sure if this is entirely correct but it is what they were thinking of.
Whoever wrote that really is a terrible teacher
1
3 years ago
#5
Is this from an A-level book? Stupid question!
0
3 years ago
#6
This doesn't make sense, you can't have a number that isnt complex?
0
3 years ago
#7
(Original post by Kalabamboo)

They say |z| is never a complex number so no possible solutions but what I don't get is how they quickly jump to this conclusion?
The argument you're quoting is wrong. It's easy (but invalid!) to quickly jump to a conclusion with a wrong argument...
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