Complex number question

[Jared123]

When I attempted it my answer was -9sqrt(2) - 9sqrt(2) and 9sqrt(2) + 9sqrt(2) which I know is wrong

 

[Romsek]

[MATH]z^2 = 36i = 36 e^{i \pi/2}[/MATH]
[MATH]z^n = r e^{i\theta} \Rightarrow z = r^{1/n} e^{i (\theta+2\pi k)/n},~k = 0, 1, \dots, n-1[/MATH]
Can you solve for \(\displaystyle z\) now?

 

[Jared123]

[MATH]z^2 = 36i = 36 e^{i \pi/2}[/MATH]
[MATH]z^n = r e^{i\theta} \Rightarrow z = r^{1/n} e^{i (\theta+2\pi k)/n},~k = 0, 1, \dots, n-1[/MATH]
Can you solve for \(\displaystyle z\) now?

thank you this helped. Im not sure if its correct but the andwer im getting now is 3 sqrt(2) + 3 sqrt(2) i and -3 sqrt(2)- 3 sqrt(2) i

 

[Dr.Peterson]

If you need additional help, please show your work, not just your answer, so we can help you identify specific errors. You may have used a different, but valid, method, and just made a silly mistake (e.g. dividing 36 by 2 instead of taking its square root).

 

[Jared123]

thank you this helped. Im not sure if its correct but the andwer im getting now is 3 sqrt(2) + 3 sqrt(2) i and -3 sqrt(2)- 3 sqrt(2) i

sorry about that. Here is my working out

 

[pka]

sorry about that. Here is my working out
View attachment 17747

Both of the above answers are correct. But you forgot to put an \(i\) in the last line in the right.
Your notation leaves much to be desired. I would write it as \(\pm(3\sqrt2+3\sqrt2\bf{i})\)

 

[topsquark]

\(\pm(3\sqrt2+3\sqrt2\bf{i})\)

Frankly I'd write it as [math] \pm (3 \sqrt{2} + 3i \sqrt{2} )[/math] to make sure it's clear that the i isn't inside the square root. But that might be a Physicist thing.

-Dan

 

[Deleted member 4993]

Frankly I'd write it as [math] \pm (3 \sqrt{2} + 3i \sqrt{2} )[/math] to make sure it's clear that the i isn't inside the square root. But that might be a Physicist thing.

-Dan

That is being kind others thing...

 

[pka]

Frankly I'd write it as [math] \pm (3 \sqrt{2} + 3i \sqrt{2} )[/math] to make sure it's clear that the i isn't inside the square root. But that might be a Physicist thing.

It may be a mathematical thing, we a accustomed to say a complex number is written as \(a+b\bf{i}\) where both \(a~\&~b\) are real numbers.
Hence \(3\sqrt2+3\sqrt2\bf{i}\).