- Proofs and Derivations (1) Given two complex numbers z 1
​
=r 1
​
(cosθ 1
​
+isinθ 1
​
) and z 2
​
=r 2
​
(cosθ 2
​
+ isinθ 2
​
), prove the following formula for the division of complex numbers. z 2
​
z 1
​
​
= r 2
​
r 1
​
​
[cos(θ 1
​
−θ 2
​
)+isin(θ 1
​
−θ 2
​
)] (2) Show that the product of z
ˉ
=r[cos(−θ)+isin(−θ)] and z=r(cosθ+isinθ) is equal to the square of the modulus.