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Let z = (sqrt(6) - sqrt(2)) + (sqrt(6) + sqrt(2))*i.  Compute z^(24).

 Aug 28, 2020
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Let z = (sqrt(6) - sqrt(2)) + (sqrt(6) + sqrt(2))*i.  Compute z^(24).

 

Convert to polar notation 

 

z = r.exp(i.θ)   where r = √(√6 - √2)2 + (√6 + √2)2 ) = 4  and  θ = tan-1( (√6 + √2)/ (√6 - √2) ) = 75°

 

z24 = r24.exp(i.24.θ) = 424.exp(1800°) = 424.(cos(1800°) + i.sin(1800°)) = 424.(cos(0°) + i.sin(0°)) = 424  

 Aug 28, 2020

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