Question

Which of the following is a complex number?

• A. $(\sec \frac{\pi }{2},i^4)$
• B. $(\sqrt{-5},i^4)$
• C. $(i^{2020},i^3)$
• D. $(i^{2022},\pi )$

Answer 1

The correct option is D $(i^{2022},\pi )$

We know that $Z\equiv (x,y)$ is complex number if $x,y\in R$

For $(\sqrt{-5},i^4)$
$(\sqrt{-5},i^4)=(i\sqrt{5},1)$
This is not a complex number.

For $(i^{2020},i^3)$
$(i^{2020},i^3)=\left(\right(i^4{)}^{505},-i)=(1,-i)$
This is not a complex number.

For $(i^{2022},\pi )$
$(i^{2022},\pi )=(i^{2020}\cdot i^2,\pi )=(-1,\pi )$
This is a complex number.

For $(\sec \frac{\pi }{2},i^4)$
We know that $\sec \frac{\pi }{2}$ is not defined.
This is not a complex number.