Algebra.Com's Answer #153909 by ptaylor(2198)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
Could you help me to understand the complex numbers formulas and specially their signs?
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document.write( "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!!!
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document.write( "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)
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document.write( "and what's the other side of (a+bi).(c-di)=?
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document.write( "cause I have :
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document.write( "about the denominator I have (a+bi).(a-bi)=a^2 + b^2
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document.write( "but there is a solved example in this site against my lecture note's formula and its examples:
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document.write( "Question 202104: (5 -i)(5 +i)= 5^2 - i^2 \r
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document.write( "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))\r
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document.write( "Forget about formulas and now lets expand (a+bi)(c+di) using FOIL:
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document.write( "ac+adi+cbi+bdi^2 (remember i^2=-1) now we have:
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document.write( "ac+(ad+cb)i-bd now we will combine the real and imaginary components:
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document.write( "(ac-bd)+(ad+cb)i\r
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document.write( "Now Let expand (a+bi)(a-bi) using FOIL:
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document.write( "(a+bi)(a-bi)=a^2-abi+abi-b^2i^2 and this equals:
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document.write( "a^2-b^2i^2 byt we know that is i=sqrt(-1), then i^2=-1, so
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document.write( "(a+bi)(a-bi)=a^2-(b^2)(-1)=a^2+b^2
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document.write( "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\r
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document.write( "hope this helps----ptaylor\r
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