If P = cos 7 2 π + i sin 7 2 π , a = P + P 2 + P 4 and b = P 3 + P 5 + P 6 , find ∣ ( a + b ) + abi ∣ .

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MathematicsComplex NumberMiscellaneous/MixedMedium2 minQB

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If $P = cos \frac{2 π}{7} + i sin \frac{2 π}{7}, a = P + P^{2} + P^{4}$ and $b = P^{3} + P^{5} + P^{6}$ , find $∣ (a + b) + abi ∣$ .

Answer:

Solution:

Since P^7=1 and P is not 1, we have a+b=-1. Also ab=2. Therefore |(a+b)+abi|=|-1+2i|=sqrt(5).

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

⏱ 2mℹ️ Source: QB

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