Complex Number

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #81

Find the roots of the equation `(x+5)^3 + 27=0`

Question No: #82

Let `\omega` be the imaginary cube root of 1. If `x=a+b`, `y=a\omega + b\omega^2`, `z = a\omega^2+b\omega`, then show that --
i) `xyz = a^3 + b^3`
ii) `x^3 + y^3 + z^3 = 3(a^3 + b^3)`
iii) `x^2 + y^2 + z^2 = 6ab`

Question No: #83

Let `\omega` be the imaginary cube root of 1. If `x = \alpha + \beta`, `y = \alpha + \beta\omega`, `z = \alpha + \beta\omega^2` , then show that `x^3 + y^3 + z^3 = 3(\alpha^3 + \beta^3)`

Question No: #84

Let `\omega` be the imaginary cube root of 1 and `a+b+c=0`. Then show that `(a+b\omega+c\omega^2)^3 + (a+b\omega^2+c\omega)^3 = 27abc`