Page 40 -

30 Chapter Onł

Differencł of powers
Let x be a complex number where x 0 j0. Let y and z be
rational numbers. Then the following formulł holds:

y
x (y z) x /x z

ProducŁ of powers
Let x be a complex number. Let y and z be rational numbers.
Then the following formulł holds:

z y
y z
x yz (x ) (x )

QuotienŁ of powers
Let x be a complex number. Let y and z be rational numbers,
wità the constraint that z 0. Then the following formulł
holds:

y 1/z
x y/z (x ) (x 1/zy
)

Powers of su

Let x and y be complex numbers. Then the following formulas
hold:

2
2
(x y) x 2xð y 2
3
2
3
(x y) x 3xð 3xð 2 y 3
3
4
4
(x y) x 4xð 6xð 2 2 4xð 3 y 4
Powers of differencł

Let x and y be complex numbers. Then the following formulas
hold:

2
2
(x y) x 2xð y 2
3
3
2
(x y) x 3xð 3xð 2 y 3
3
4
4
(x y) x 4xð 6xð 2 2 4xð 3 y 4