Advanced Math/Relations( concerning sets)
I've started doing sums from 11th grade books and in the second chapter concerning relations between sets have given me a doubt. Here's the same.
"A relation A(name of relation set) from C to R is defined by x A y <=> |x| =y. Which one is correct:
where C= the set of complex numbers
and R=the set of real numbers.
The modulus of a complex number z = a + bi is given by the positive value of
|z| = √(a² + b²)
So, for x = 2 + 3i
|x| = √(2² + 3²) = √13
which is not the same as 13, and so option 1 is wrong
Option 2 is definitely wrong since |x| can only be a positive number.
Option 3 is wrong too as |x| = √2
Lastly, for x = i (which is the same as x = 0 + 1i)
|x| = √(0² + 1²) = 1
and so option 4 is the correct answer.