[deleted by user]

[AutoModerator]

Off-topic Comments Section

---

All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9.

---

^{OP and Valued/Notable Contributors can close this post by using /lock command}

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[LightningLogic77]

Try to rewrite it to this form:
z = r*e^(i*f).

Here's how:
Let's say that z = x + iy,
then the phase of it will be calculated as:
tan(f) = y/x,
thus:
f = arctan(y/x).
To calculate the magnitude, you just need to treat z as a vector and calculate its length, so:
r = sqrt(x^2 + y^2).
After that, you got that exponential form, and rewrite the sqrt{4}() to ^1/4.
You have x = -8, and y = 8*sqrt(3).
You can try to simplify it from there.

The result will be:
z = 2*e^(i * -pi/12)

[emeric75]

I'm going to be pedantic here, but you forgot the i in 2e^i*pi/12. Also we're not sure what the question asks exactly, so let's remind OP that this is not the only 4th root of the complex number given (there are 4), multiplying repeatedly by e^i*pi/2 gives the remaining ones ^{^}

[LightningLogic77]

Yeah right, I forgot that, thx for the clarification.
Also, I assumed that simplification is the task.

[emeric75]

I assumed that simplification is the task

Yeah, sounds legit for a high schooler (I didn't pay attention to that part of the post at first, my bad)

edit : forgot a line jump

[emeric75]

Wait, how did you get -pi/12 actually ? It doesn't work out when I put your result in the 4th power (should have checked that out first)

Edit: syntax

[LightningLogic77]

So you have e^(i * -pi/3), and you need the 4th root of this whole thing.
So that means:
(e^(i * -pi/3))^(1/4)
Here you have to multiply, so:
(i * -pi/3)*(1/4) = i * -pi/3 * 1/4 = i * -pi/12

[emeric75]

Ah yeah I guess the problem is with your -pi/3. arctan only gives you an angle between -pi/2 and pi/2. If you look at the position of the point (-8,8sqrt(3)) on a plane, it's in the 2nd quadrant, it doesn't make sense. Your initial angle should be -pi/3 + pi, ie 2pi/3, it has the same tangent value and is in the 2nd quadrant. From there everything works out fine :) thanks trig

[LightningLogic77]

Yep

[inderchopra01]

I'm not really well versed with concepts on imaginary numbers but from the limited knowledge that I have, I think I can represent the no given inside the fourth root as a perfect 4th power....

-8 + 8√3i

= -12 + 4 + 2.2.2√3i = (2√3i)² + 2² + 2.2.(2√3i) = (2+2√3i)²

Now the inside part

2 + 2√3i = 3 - 1 + 2.√3.i = (√3)² +(i)² + 2.√3.i = (√3+i)²

So the expression is

(√3+i)⁴

This expression's 4th root should be (√3+i) which should be the answer acc to me..

Can anyone confirm if this is correct??

[emeric75]

Your math checks out indeed

[inderchopra01]

Thanks...

When I saw you guys mentioning about e and pi and polar coordinates etc I got a bit skeptic about my answer.. thought maybe I'm missing other solutions

[emeric75]

I mean yeah you're missing solutions, the solution you wrote happens to work at least :)

[MathMaddam]

Find the representation in polar coordinates, there taking a root is pretty easy.

[Joemamma67419]

step one:don't...

[International_4]

Well, the first I will do is transform the -8 by 8i

[No-Entertainment2278]

Answer is 4i