If z = 2 + 3 i , then z 5 + z ¯ 5 is equal to:

Given z = 2 + 3 i , So, z 5 + z ¯ 5 = 2 + 3 i 5 + 2 - 3 i 5 Applying binomial expansion we get, = 2 C 0 5 2 5 + C 2 5 2 3 3 i 2 + C 4 5 2 1 3 i 4 = 2 32 + 10 × 8 - 9 + 5 × 2 × 81 = 244

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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Easy2 minPYQ_2022

MathematicsEasysingle choice

If $z = 2 + 3 i$ , then $z^{5} + {(\bar{z})}^{5}$ is equal to:

Options:

Answer:

Solution:

Given $z = 2 + 3 i$ ,
So, $z^{5} + {(\bar{z})}^{5} = {(2 + 3 i)}^{5} + {(2 - 3 i)}^{5}$
Applying binomial expansion we get,
$= 2 ({}^{5}C_{0} 2^{5} + {}^{5}C_{2} 2^{3} {(3 i)}^{2} + {}^{5}C_{4} 2^{1} {(3 i)}^{4})$
$= 2 (32 + 10 \times 8 (- 9) + 5 \times 2 \times 81) = 244$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2022

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