# Thread: Can someone check my Trig (Trig Form and Demoive's Theorm

1. ## Can someone check my Trig (Trig Form and Demoive's Theorm

Hi can someone check this to see if it's correct.

Trig Form

(4-3i) into Trig form

r= Sqrt (4^2+(-3)^2
r= Sqrt (25)
r= 5

tan = -(3/4) = -.01309
arctan = -.74995
2pi -.74995
= 5.5332

Z= 5 (cos 5.5332 + i sin 5.5332)
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I got confused with the Demoive question

(11+i)^6

r= Sqrt (11^2+1)
r= Sqrt (122)

tan 1/11 = .001586 <----- Is this right?
arctan (.001586) = .09087103
2pi + .09087103
= 6.19231

Put it into Trig form
Z= Sqrt(122) (cos 6.19231 + i sin 6.19231)

Demoiver's

z^6 = Sqrt (122)^6 (cos 6.19231 + i sin 6.19231) ......

First I don't even know if that is right. Also, if it is right I do not know the next step to completing the problem.

Thanks

2. Originally Posted by killasnake
Hi can someone check this to see if it's correct.
(4-3i) into Trig form

r= Sqrt (4^2+(-3)^2
r= Sqrt (25)
r= 5

tan = -(3/4) = -.01309
arctan = -.74995
2pi -.74995
= 5.5332

Z= 5 (cos 5.5332 + i sin 5.5332)

I got confused with the Demoive question

(11+i)^6

r= Sqrt (11^2+1)
r= Sqrt (122)

tan 1/11 = .001586 <----- Is this right?
arctan (.001586) = .09087103
2pi + .09087103
= 6.19231

Put it into Trig form
Z= Sqrt(122) (cos 6.19231 + i sin 6.19231)

Demoiver's

z^6 = Sqrt (122)^6 (cos 6.19231 + i sin 6.19231) ......

First I don't even know if that is right. Also, if it is right I do not know the next step to completing the problem.

Thanks
1)
So you're saying that the trig form is z = r cis theta.

You found r to be 5.
You faultered on the theta.
tan(theta) = -3/4 = -0.75 --------not -0.01309.
So, theta = arctan(-0.75) = -0.6435 radians.
Or, if you want positive theta,
theta = -0.6435 == 2pi -0.6435 = 5.6397 radians

Check,
Yes, so, OK.
---------------------------
2)
You're having problem with your theta.
What is tan (1/11)? The (1/11) is a ratio, not an angle.
It shoud be tan(theta) = 1/11.
Then theta = arctan(1/11) = arctan(0.09090909...) = 0.09066 radian
So, 11 +i = sqrt(122) cis 0.09066
Then,
(11 +i)^6
= [sqrt(122)]^6 cis (0.09066 *6)