Let p and q be complex numbers with q ≠ 0. Prove that if the roots of the quadratic equation have the same absolute value then is a real number
My Self Assessment
Determine the values of α, β, γ when is orthogonal.
a)
b)
c)
d)
If choose α and β such that .
a) α = β = ± 1
Write the following transformation in matrix form : . Hence find the transformation in matrix form which expresses in terms of .
If and I is a unit matrix then is equal to
a) I + A
b) A
c) I – A2
d) I + A2
If then show that where n is a positive integer.
If then show that
Show that
Simplify
Compute where
Compute
Prove that
Prove the following identity
Let z ℂ such that . Prove that
Find all complex numbers such that
Consider z ℂ with Re (z) > 1. Prove that
Let a, b, c be real numbers and . Compute
is orthogonal.
