Let z be a complex number, then the equation | vedclass

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Question

(a)Suppose there exists a complex number $z$ which satisfies the given equation and is such that $|z|\, < 1$.
Then ${z^4} + z + 2 = 0$ ==> $ -

Vedclass · Accepted Answer

$|z|\, < 1$

Vedclass · Answer

(a)Suppose there exists a complex number $z$ which satisfies the given equation and is such that $|z|\, < 1$. Then ${z^4} + z + 2 = 0$ ==> $ - 2 = {z^4} + z$==> $| - 2|\, = \,|{z^4} + z|$ ==> $2 \le \,|{z^4}| + |z|$==> $2 < 2,$ because$|z|\, < 1$ But $2 < 2$ is not possible. Hence given equation cannot have a root $z$ such that $|z| < 1$

Let $z$ be a complex number, then the equation ${z^4} + z + 2 = 0$ cannot have a root, such that

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