One of The "Easiest" IIT Math Problem I Have Ever Solved!

Let a, b, c and d be complex numbers satisfying the following two equations, a + b + c + d = a^3 + b^3 + c^3 + d^3 = 0.
Can you prove that a pair of the complex numbers a, b, c and d must add up to 0? This is a problem from an IIT exam in 1994 which I think is a university entrance exam in India, although I am not too sure about that.
Well, comment down below if you are from India.
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Video Chapters:
0:00 1994 IIT Math Exam Problem
0:33 Idea + Motivation
1:05 Solution
1:58 Factorisation
4:11 Solution Continued
5:26 Outro + Subscribe!
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[@Ki0212]

Hey! From India here.
This sounds too easy for iit jee lol

[@1psi3colourmath]

I'll build up the difficulty of the problems, there will be more challenging problems in the future!

[@unknownuserallday]

@@1psi3colourmath hi can u help me understand the base of algebra expand equation?

[@1psi3colourmath]

@@unknownuserallday Hi, one way you can get the expansion is by multiplying out the terms,
(a+b+c)(a+b+c)(a+b+c)
=(a²+b²+c²+2ab+2bc+2ca)(a+b+c)
=a³+b³+c³+3(a²b+ab²+b²c+bc²+c²a+ca²)+6abc

[@unknownuserallday]

@@1psi3colourmath that's the thing i confusing , I can't understand the base of it and next week exam, teacher said paper got 50+ pages

[@midnightgamer4201]

i dont think that this problem was easy even with iit jee standards