If z = 2 3 + i , find ( z 101 + i 103 ) 105 .

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MathematicsComplex NumberMiscellaneous/MixedMedium2 minQB

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If $z = \frac{3 + i}{2}$ , find $(z^{101} + i^{103})^{105}$ .

Answer:

Solution:

Here z=exp(i pi/6). Reducing powers gives z^101+i^103=i omega, so its 105th power is i=z^3.

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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