Question

Find the number of different ordered quadruples (a,b,c,d) of complex numbers such that
a^2=1
b^3=1
c^4=1
d^6=1
a+b+c+d=0

Answer 1

visit wolframalpha.com and enter

solve a^2=1, b^3=1, c^4=1, d^6=1, a+b+c+d=0

and you can check your details.

Answer 2

There are 3 solutions with real numbers and 4 solutions with complex numbers