Can someone explain how to express -4 in trigonometric form? Really lost. Thank you!

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Can someone explain how to express -4 in trigonometric form? Really lost. Thank you!

Mathematics
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Polar form: \(\Large (r,\theta)\) Trig form: \(\Large r[\cos(\theta) + i*\sin(\theta)]\) The two forms are very similar
write -4 as -4+0i that is in the form a+bi
Ok.

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a = -4 b = 0 plug those values into the formulas r = sqrt(a^2 + b^2) theta = arctan(b/a)
So r = 4 and theta = 0?
r = 4 is correct but theta = 0 is not
|dw:1437696080574:dw|
Isn't 0/-4 equal to 0, and the arctan(0) just 0?
arctan(b/a) = arctan(0/(-4)) = 0 is true but we're in the wrong spot add on 180 degrees |dw:1437696139033:dw|
So is r = 4 and theta = -4...?
theta = 180 degrees = pi radians
so theta = pi ?
yeah
Ok so let me try and see if I can get the answer.
A. 4(cos0degrees + i sin270degrees) B. 4(cos90degrees + i sin90degrees) C. 4(cos0degrees + i sin0degrees) D. 4(cos180degrees + i sin180degrees) Would it be D?
The trig form, in radians, is \(\Large 4[\cos(\pi) + i*\sin(\pi)]\) that's equivalent to \(\Large 4[\cos(180^{\circ}) + i*\sin(180^{\circ})]\)
you are correct
Thank you! I'll Medal you (:
you're welcome
Could you help me do the same thing for -6i?
-6i = 0 + (-6i) now a = 0 and b = -6
use the formulas r = sqrt(a^2 + b^2) theta = arctan(b/a)
draw a graph to make sure you get the theta in the right spot
So would theta = pi?
what is the value of b/a this time?
Undefined actually
where is tan(theta) undefined?
Isn't it at 90 degrees and 270 degrees?
correct
|dw:1437697203957:dw|
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So theta = 3pi/2
yep
Therefore making the answer: 6(cos270degrees + i sin270degrees)
correct
Thank you so much, could you help me with just one more? I think I understand how to do a single number, but am not sure how to do an equation?
what's the question
3-3i
that's not an equation. An equation needs an = sign
Sorry, meant expression.
compare a+bi with 3-3i to see that a = 3 and b = -3
Oh ok! So then r = 3SqRt2 and theta = -1 ... but I'm still confused as to how you find the theta degree value.
theta is not -1
b/a = -1, that is true
arctan(b/a) = arctan(-1) = ??
-45...
So 315 degrees?
yes
So would the answer be: 3SqRt2(cos7pi/4 + i sin7pi/4) ?
correct
Thank you so much. I finally understand this!! (: You really helped me understand this, if I could give you more medals I definitely would.
that would be the radian form
you're welcome
Yes, that is what the answers are listed as.

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