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heureka

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 #1
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Hi I was looking for steps to show z=sin(i ln(2)) + cos(i ln(2)) = 5/4 +3i/4

 

 sinz=12i(eixeix)cosz=12(eix+eix) 

 

sin(iln(2))=12i(eiiln(2)eiiln(2))=12i(eln(2)eln(2))ii=i2=1cos(iln(2))=12(eiiln(2)+eiiln(2))=12(eln(2)+eln(2))ii=i2=1sin(iln(2))+cos(iln(2))=12i(eln(2)eln(2))+12(eln(2)+eln(2))=12i(eln(2)eln(2))ii+12(eln(2)+eln(2))=i2(eln(2)eln(2))+12(eln(2)+eln(2))=12(eln(2)+eln(2))i2(eln(2)eln(2))eln(2)=2eln(2)=1eln(2)=12sin(iln(2))+cos(iln(2))=12(12+2)i2(122)=54i2(32)=54+i(34)

 

laugh

25.02.2016
 #1
avatar+26396 
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9l9-8xl=2x+3 it saids extraneous solution? can someone teach me step by step to solve this?

 

9|98x|=2x+3|(square both sides)92(98x)2=(2x+3)281(92298x+82x2)=22x2+223x+3281(81144x+64x2)=4x2+12x+981281144x+8164x2=4x2+12x+9656111664x+5184x2=4x2+12x+9|4x2656111664x+5180x2=12x+9|12x656111676x+5180x2=9|9655211676x+5180x2=05180x211676x+6552=0|:41295x22919x+1638=0

 

 ax2+bx+c=0x=b±b24ac2a 

 

1295x22919x+1638=0|a=1295b=2919c=1638x=(2919)±(2919)241295163821295x=2919±852056184848402590x=2919±357212590x=2919±1892590x1=2919+1892590x1=31082590x1=1.2x2=29191892590x2=27302590x2=273259x2=1.¯054

 

laugh

25.02.2016