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Question
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:
1. (2+3i)A13
2. 3A(-3)
3. (1+i)A2
4. iA1

where C= the set of complex numbers
and R=the set of real numbers.

Sincerely yours,
AB.

Hi AB,

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.

Regards

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