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Suppose $a < 0$ and $z_{1}, z_{2}, z_{3}, z_{4}$ $4$ be the fourth roots of a then $z_{1}^{2} + z_{2}^{2} + z_{3}^{2} + z_{4}^{2}$ is equal

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detailed solution

Correct option is C

Let a=−b4 where b>0. Than z4=a=b4(−1) ⇒z =b±cos⁡π4±isin⁡π4 ∴ z12+z22+z32+z42 =2b2cos⁡π2−isin⁡π2+cos⁡π2+isin⁡π2 =0=a+|a| [∵a<0]

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Suppose a<0 and z1,z2,z3,z4 4 be the fourth roots of a then z12+z22+z32+z42 is equal

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Ready to Test Your Skills?

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Suppose $a < 0$ and $z_{1}, z_{2}, z_{3}, z_{4}$ $4$ be the fourth roots of a then $z_{1}^{2} + z_{2}^{2} + z_{3}^{2} + z_{4}^{2}$ is equal