1. Tardigrade
  2. Question
  3. Mathematics
  4. Which of the following are correct? I. A number in the form of x+i y, where x, y ∈ R, is a complex number. II. If z=x+i y and x=0, then complex number is purely imaginary. III. If z=x+i y and y=0, then complex number is purely real.

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Q. Which of the following are correct?
I. A number in the form of $x+i y$, where $x, y \in R$, is a complex number.
II. If $z=x+i y$ and $x=0$, then complex number is purely imaginary.
III. If $z=x+i y$ and $y=0$, then complex number is purely real.

Complex Numbers and Quadratic Equations

Solution:

If $z=x+i y$ is a complex number and if $x=0$, then $z=i y$, which is purely imaginary and if $y=0$, then $z=x$ which is purely real.