$\mathrm{\alpha }\ne 1\text{ is a }{5}^{\text{th }}$ root of 1 and $\mathrm{\beta }\ne -1$ is a 5th root of –1. Which of the following assertions is (are) true?

$(\mathrm{\alpha \beta }{)}^5={\mathrm{\alpha }}^5{\mathrm{\beta }}^5=-1$is true ${\left({\mathrm{\alpha }}^2\mathrm{\beta }\right)}^5={\mathrm{\alpha }}^{10}{\mathrm{\beta }}^5=-1$
(b) is false Since $(\mathrm{\alpha \beta }{)}^5=-1\therefore |\mathrm{\alpha \beta }|=1$ (c) is true
Finally,  $|\mathrm{\alpha }+\mathrm{\beta }|<\left|\mathrm{\alpha }\right|+\left|\mathrm{\beta }\right|=1+1$ (d) is true (Equality is not possible since $\mathrm{\alpha }$ and $\mathrm{\beta }$ do not have the same arg.)