How do I evaluate this? #|(1+i)^50|#

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Answer 1 · 2018-02-25T14:09:39

#abs((1+i)^50) = 33554432#

Note that:

#abs(1+i) = sqrt(1^2+1^2) = sqrt(2)#

Note also that:

#abs(ab) = abs(a) abs(b)#

and hence:

#abs(a^n) = (abs(a))^n#

So we find:

#abs((1+i)^50) = (abs(1+i))^50 = (sqrt(2))^50 = 2^(50/2) = 2^25 = 33554432#