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

b)

c)

d)

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

Simplify

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

Compute  where

Compute  where

Compute   

Compute   where

Prove that  

Prove that  

Prove the following identity
 

Prove the following identity
 

Prove the following identity

Find all complex numbers such 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