A little help with this complex number question

[aerosmith]

if z = 2 r cos x + r i sin x
what is the value of lzl

I worked for 3 hours but yet can only find lzl in terms of r and x, but the question says find the value, can anyone help solve? this is a special question to me because i always see polar forms with coefficient of the sin and cos as the same, but this question shows otherwise.

ty, help appreciated.

 

[FunkyDwarf]

you sure you don't mean z = 2rCos(x) + riSin(x) ? If so use your Cis rule or exponential equality for cos + i sin

 

[aerosmith]

sorry bout the i, i edited already, what do u mean by the cis rule or exponential equality, can u teach me?

 

[aerosmith]

can anybody help solve this for me?

 

[HallsofIvy]

Am I correct, that you are given z= 2r cos(x)+ i r sin(x) and want to find |z|? That will depend on r and x- it's obviously not a single number since the larger r is obviously the larger the |z|. If, for example, x= 0 then z= 2r which has absolute value 2r. If x= \frac{\pi}{2} then z= i r and so |z|= r.

|z|= \sqrt{z\cdot\overlinez}= \sqrt{(2r cos(x)+ i r sin(x))(2r cos(x)- i r sin(x)}= \sqrt{4r^2cos^2(x)- r^2 sin^2(x)}[/= r \sqrt{4 cos^2(x)- sin^2(x)}

You might be able to simplify that squareroot by trig identities but you can't get rid of r and x.

 

[FunkyDwarf]

the cis thing is basically converting complex cartesian forms to polar ones

{e^{it}} = Cos(t) + i Sin(t)

the t should be the power as well with i but for some reason the tex won't do it :( need to learn more about it i guess

 

[aerosmith]

ok, so now i know i was right, time to get to school and prove to my teacher that there is no answer, since the question asks for a value, ty ppl for helping me, i wasted 5 hours of my life working on something i got right 5 hours ago, once again ty ppl, help appreciated.