Hi, all, i'm struggling to solve this complex number.
[math]((\frac{\sqrt 3}{2}+\frac{i}{2})^{2021}+(\frac{\sqrt 3}{2}-\frac{i}{2})^{2021})[/math]
I don't know how to go with this one in my math workbook (college)
I don't know how i can add them (like they are usually added, real with real, and imaginary with imaginary), if i add them usual way, i get, Imaginary part to be 0
But when i insert this problem in calculator, i get -1.73
Also, this big square (2021) is confusing me even more)
I tried to put it in polar form, and somehow to get rid of 2021 first, but, i can't finish it, because i get very weird numbers (or is it's because i put them wrong way in calculator?)
When trying to put it in polar form, only this i can get right is intensity, which is 1, but i dont know how to get angle.
I tried to get angle with putting [math]\frac{cos \frac{1}{2}}{sin \frac{\sqrt 3}{2}}[/math] because [math]tan^{-1}[/math] is [math]\frac{cos}{sin}[/math]And i get [math]\frac{1}{0.021}[/math] which i then calculate and get 46.78 degrees
But that look wrong. Because, on calculator i got -1.73
That doesn't look like good way to get that angle.
So, my biggest problem and question here, is, how to get angle right, and how to sum them (maybe, polar form is not needed?) ?
Because, this 2021, i think it's done, by simplifyning, because it goes into circles . it would be 5 i think.
But without getting angle right way, or, how to add them at all, i can't solve this at all.
[math]((\frac{\sqrt 3}{2}+\frac{i}{2})^{2021}+(\frac{\sqrt 3}{2}-\frac{i}{2})^{2021})[/math]
I don't know how to go with this one in my math workbook (college)
I don't know how i can add them (like they are usually added, real with real, and imaginary with imaginary), if i add them usual way, i get, Imaginary part to be 0
But when i insert this problem in calculator, i get -1.73
Also, this big square (2021) is confusing me even more)
I tried to put it in polar form, and somehow to get rid of 2021 first, but, i can't finish it, because i get very weird numbers (or is it's because i put them wrong way in calculator?)
When trying to put it in polar form, only this i can get right is intensity, which is 1, but i dont know how to get angle.
I tried to get angle with putting [math]\frac{cos \frac{1}{2}}{sin \frac{\sqrt 3}{2}}[/math] because [math]tan^{-1}[/math] is [math]\frac{cos}{sin}[/math]And i get [math]\frac{1}{0.021}[/math] which i then calculate and get 46.78 degrees
But that look wrong. Because, on calculator i got -1.73
That doesn't look like good way to get that angle.
So, my biggest problem and question here, is, how to get angle right, and how to sum them (maybe, polar form is not needed?) ?
Because, this 2021, i think it's done, by simplifyning, because it goes into circles . it would be 5 i think.
But without getting angle right way, or, how to add them at all, i can't solve this at all.