Question

If $z$ is a complex number satisfying the equation $z^6-6z^3+25=0$, then the value of $\left|z\right|$ is

• A. $5^{1/3}$
• B. ${25}^{1/3}$
• C. ${125}^{1/3}$
• D. ${625}^{1/3}$

Answer 1

Answer: (A)

$5^{1/3}$

Given, $z^6-6z^3+25=0$

Put $z^3=t$

$\Rightarrow$ $t^2-6t+25=0$

$\Rightarrow$ $t=\frac{6\pm \sqrt{-64}}{2}=3\pm 4i$

$\Rightarrow$ $z={(3\pm 4i)}^{1/3}$

$\Rightarrow$ $\left|z\right|={|3+4i|}^{1/3}$

$|z|={\left(\sqrt{3^2+4^2}\right)}^{1/3}$

$|z|=5^{1/3}$