SOLUTION: Could you help me to understand the complex numbers formulas and specially their signs?
Do I must commit all to memory or there are some correspondences between them? I compared s
Question 203990: Could you help me to understand the complex numbers formulas and specially their signs?
Do I must commit all to memory or there are some correspondences between them? I compared some of mine with some of solved ones here but they were absolutly different with my formulas!!!
I have (a+bi).(c+di)=(ac-bd).(ad+bc)i [why both sides are multiplay and why we have minus in the other side?!]
and what's the other side of (a+bi).(c-di)=?
cause I have :
about the denominator I have (a+bi).(a-bi)=a^2 + b^2
but there is a solved example in this site against my lecture note's formula and its examples:
Question 202104: (5 -i)(5 +i)= 5^2 - i^2
You can put this solution on YOUR website! Could you help me to understand the complex numbers formulas and specially their signs?
Do I must commit all to memory or there are some correspondences between them? I compared some of mine with some of solved ones here but they were absolutly different with my formulas!!!
I have (a+bi).(c+di)=(ac-bd).(ad+bc)i [why both sides are multiplay and why we have minus in the other side?!] NEED TO RECHECK THIS!!! SEE BELOW)
and what's the other side of (a+bi).(c-di)=?
cause I have :
about the denominator I have (a+bi).(a-bi)=a^2 + b^2
but there is a solved example in this site against my lecture note's formula and its examples:
Question 202104: (5 -i)(5 +i)= 5^2 - i^2
LOOKS TO ME LIKE YOU ARE GIVING IT A GOOD SHOT. IN MY VIEW, THE ONLY THING THAT YOU HAVE TO COMMIT TO MEMORY IS THE FACT THAT i WHICH IS AN IMAGINARY NUMBER=sqrt(-1)and and it follows that i^2=-1. Complex numbers have both real and imaginary components and we have to keep the real components and the imaginary components separate (e.g., (a+bi))
Forget about formulas and now lets expand (a+bi)(c+di) using FOIL:
ac+adi+cbi+bdi^2 (remember i^2=-1) now we have:
ac+(ad+cb)i-bd now we will combine the real and imaginary components:
(ac-bd)+(ad+cb)i
Now Let expand (a+bi)(a-bi) using FOIL:
(a+bi)(a-bi)=a^2-abi+abi-b^2i^2 and this equals:
a^2-b^2i^2 byt we know that is i=sqrt(-1), then i^2=-1, so
(a+bi)(a-bi)=a^2-(b^2)(-1)=a^2+b^2
Regarding Question 202104: (5 -i)(5 +i)= 5^2 - i^2. Here again i^2=-1, so we have 5^2-(-1)=5^2+1=26 which is the answer the tutor came up with
