# A little help with this complex number question

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.

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## Answers and Replies

you sure you dont mean $$z = 2rCos(x) + riSin(x)$$ ? If so use your Cis rule or exponential equality for cos + i sin

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

can anybody help solve this for me?

HallsofIvy
Science Advisor
Homework Helper
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.

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 aswell with i but for some reason the tex wont do it :( need to learn more about it i guess

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.