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

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

Let z   ℂ such that . Prove that

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