A) \[|z|\,<1\]
B) \[|z|\,=1\]
C) \[|z|\,>1\]
D) None of these
Correct Answer: A
Solution :
Suppose there exists a complex number \[z\] which satisfies the given equation and is such that \[|z|\,<1\]. Then \[{{z}^{4}}+z+2=0\] Þ \[-2={{z}^{4}}+z\]Þ \[|-2|\,=\,|{{z}^{4}}+z|\] Þ \[2\le \,|{{z}^{4}}|+|z|\]Þ \[2<2,\] because\[|z|\,<1\] But \[2<2\] is not possible. Hence given equation cannot have a root \[z\] such that \[|z|<1\]You need to login to perform this action.
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