Another Complex Number Question... (2 Viewers)

[ella-m]

thanks all!!
xx

 

[ohexploitable]

 

[Bored Of Fail 2]

finding th modulus for 35 is fairly standard, just mod = sqrt ( (real part)^2 + (imag part)^2 )

= sqrt ( ( 1+cosx)^2 + (sin(x))^2 ) = sqrt ( 2 +2cosx )

then using double angle results cosx = 2 (cos(x/2) )^2 -1 , then sub in and mod is done

argument is a fair bit harder

 

[ohexploitable]

 

[ohexploitable]

 

[ohexploitable]

 

[Bored Of Fail 2]

when you go from sin (x/2) / cos ( x/2) = sqrt ( (1-cosx)/ ( 1+cosx) ) I think I kinda know what did , but im thinking there is 90% chance that the person that asked the question has no idea what you did lol

Also, I must say I am very impressed someone doing gen maths could do these questions

 

[ohexploitable]

 

[Bored Of Fail 2]

ahh I gotcha, and the third part to that questions is relatvely easy,

just a fairly standard binomial question where you take n=4

ie consider ( 1 + ( cosx+ i sinx ) ) ^4 and then expand it using binomial theorm and use the theorm ( cos(x) + isin(x) ) ^n = cos(nx) + i sin(nx)

then equate real and imaginary parts

etc
etc

but most 4unit students wouldnt have seen that yet, most school leave binomial theorm as the last chapter of 3unit math

 

[ella-m]

Thanks Heapppss bored of fail 2 & ohexploitable.... your help is much appreciated

 

[ella-m]

but can you also do 34 part ii?

 

[Bored Of Fail 2]

but can you also do 34 part ii?

following from that.

now it tells us that this is a real number/expression ( it says z + 1/z = k, where k is real )

so that means its imaginary part must be zero

therefore y ( x^2 +y^2 -1) / ( x^2 + y^2 ) =0

and setting each factor equal to zero gives

y=0 , or x^2 +y^2 =1

im so cluesless on the other part :|, been try to sub in the values and shit and still cnt get anywhere

 

[deterministic]

Suppose y=0, then z+1/z=x+1/x=k
so |k|=|x+1/x|=|(x^2+1)/x|
we use the basic inequality of x^2+1>=2x (Based on (x-1)^2>=0)
Then |k| = |(x^2+1)/x| >= |(2x)/x|=2 so |k|>=2

Suppose x^2+y^2=1:
Then |x|<=1 (as x and y are real numbers)
so subbing (x^2+y^2=1) into the equation for k will give us:
k= x(1+1)/1= 2x
Since |x|<=1, then |k|= |2x|=2|x|<=2*1=2 so |k|<=2

 

[ohexploitable]

Suppose y=0, then z+1/z=x+1/x=k
so |k|=|x+1/x|=|(x^2+1)/x|
we use the basic inequality of x^2+1>=2x (Based on (x-1)^2>=0)
Then |k| = |(x^2+1)/x| >= |(2x)/x|=2 so |k|>=2

Suppose x^2+y^2=1:
Then |x|<=1 (as x and y are real numbers)
so subbing (x^2+y^2=1) into the equation for k will give us:
k= x(1+1)/1= 2x
Since |x|<=1, then |k|= |2x|=2|x|<=2*1=2 so |k|<=2

I gave your post some protection

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[ella-m]

I gave your post some protection

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Rofls ! thanks for your help... and the protection