Answer:
Let be a rational complex number of the form 
, we proceed to show the procedure of resolution by algebraic means:
1) 
Given.
2) 
Modulative property.
3) 
Existence of additive inverse/Definition of division.
4) 
5) 
Distributive and commutative properties.
6) 
Distributive property.
7) ![\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Ccdot%20c%20%2Bi%5C%2C%28-a%5Ccdot%20d%29%20%2B%20i%5C%2C%28b%5Ccdot%20c%29%20%2B%28-i%5E%7B2%7D%29%5Ccdot%20%28b%5Ccdot%20d%29%7D%7Bc%5E%7B2%7D%2Bi%5C%2C%28c%5Ccdot%20d%29%2B%5B-i%5C%2C%28c%5Ccdot%20d%29%5D%20%2B%28-i%5E%7B2%7D%29%5Ccdot%20d%5E%7B2%7D%7D)
Definition of power/Associative and commutative properties/
/Definition of subtraction.
8) 
Definition of imaginary number//Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.
Step-by-step explanation:
Let be a rational complex number of the form , we proceed to show the procedure of resolution by algebraic means:
1) Given.
2) Modulative property.
3) Existence of additive inverse/Definition of division.
4)
5) Distributive and commutative properties.
6) Distributive property.
7) Definition of power/Associative and commutative properties//Definition of subtraction.
8) Definition of imaginary number//Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.
