Prove by the principle of Mathematical induction | 1^3 + 2^3 + 3^3 + …. + n^3 == [(n(n+1))/2]^2

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Prove by the principle of Mathematical induction for all n belongs to N |
1^3 + 2^3 + 3^3 + …. + n^3 == [(n(n+1))/2]^2 | Mathematical Induction | Maths
Mathematical Induction | Class 11 | Principle of Mathematical Induction

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7. Solve the following equations in the set of complex numbers: (a) z^(3/2) =8i (b), z^5 = −2−2i. Please do this one, it is my assignment for tomorrow.

[@hi-qlearning]

z^(3/2)=8i
or, z= (8i)^(2/3)
=8^(2/3) i^(2/3)
= 4 (-1)^(1/3)------(1)
Let (-1)^(1/3) =x
or, x^3 =-1
or, x^3 +1 =0
or, (x+1)(x^2-x+1)=0
So, x=-1 or, x^2-x+1=0
or, x=[1+-(1-4)(1/2)]/2
or, x=1/2+[3^(1/2)i]/2
and x=1/2-[3^(1/2)i]/2
and x=-1

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