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Complex variables

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if alpha and beta are imaginary cube roots of unity then find the value of Alpha power 4 + beta power 4 + alpha beta

ARYAN SAGAR 11th Jan, 2021

Dear student,

The cube roots of unity are 1, w, w^2.
And according to the property of cube roots of unity :- 1 + w + w^2 = 0

Now, if alpha and beta are imaginary cube roots of unity, so take alpha as w and beta as w^2 (

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find valu of x and y . x+y iota upon 2+3iota + 2+iota upon 2-3iota = 9 upon13 (1+iota)

Anuj More 19th Oct, 2020

Dear Student,

You can find the values of x & y by multiplying & dividing (2-3i) to the first term (i.e by its complex conjugate) & multiply & divide second term by (2+3i) (complex conjugate of 2-3i). Similarly solve the equations on LHS till you get an equation in terms

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