If z is a complex number satisfying |z|^2 - | | vedclass

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Question

$|z|^{2}-|z|-2<0$

$\Rightarrow(|z|-2)(|z|+1)<0 \Rightarrow|z|<2$

Now $\left| {{z^2} + z\sin 	heta } ight| \le {\left| z ight|^2} +

Vedclass · Accepted Answer

less than $6$

Vedclass · Answer

$|z|^{2}-|z|-2<0$

$\Rightarrow(|z|-2)(|z|+1)<0 \Rightarrow|z|<2$

Now $\left| {{z^2} + z\sin 	heta } ight| \le {\left| z ight|^2} + |z\sin 	heta | \le |z{|^2} + |z| < 4 + 2 = 6$

If $z$ is a complex number satisfying $|z|^2 - |z| - 2 < 0$, then the value of $|z^2 + z sin \theta|$ , for all values of $\theta$ , is

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