Relation from Complex Numbers to Real Numbers | Modulus Relation
Question
A relation \( \phi \) from \( C \) to \( R \) is defined by
\[ x\phi y \iff |x|=y \]
Which one is correct?
(a) \( (2+3i)\phi13 \)
(b) \( 3\phi(-3) \)
(c) \( (1+i)\phi2 \)
(d) \( i\phi1 \)
Solution
\[ |2+3i|=\sqrt{2^2+3^2}=\sqrt{13}\ne13 \]
\[ |3|=3\ne-3 \]
\[ |1+i|=\sqrt{1^2+1^2}=\sqrt{2}\ne2 \]
\[ |i|=1 \]
Hence, \[ i\phi1 \] is correct.
Therefore, the correct answer is (d).