We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
86
3
avatar

There are four different fourth roots of 16. That is, there are four complex numbers that can be x in the equation below:

x^4=16 

What are the four complex numbers?

 Sep 25, 2019
edited by Guest  Sep 25, 2019

Best Answer 

 #1
avatar+6045 
+1

\(16 = 16 e^{i 2\pi k},~k \in \mathbb{Z}\\ \sqrt[4]{16} = \sqrt[4]{16}e^{i \frac{2\pi k }{4}},~k = 0, 1, 2, 3 = \\ 2e^{0},~2e^{i\pi/2},~2e^{i\pi},~2e^{i3\pi/2} = \\ 2, 2i, -2, -2i\)

.
 Sep 25, 2019
 #1
avatar+6045 
+1
Best Answer

\(16 = 16 e^{i 2\pi k},~k \in \mathbb{Z}\\ \sqrt[4]{16} = \sqrt[4]{16}e^{i \frac{2\pi k }{4}},~k = 0, 1, 2, 3 = \\ 2e^{0},~2e^{i\pi/2},~2e^{i\pi},~2e^{i3\pi/2} = \\ 2, 2i, -2, -2i\)

Rom Sep 25, 2019
 #2
avatar+2361 
+1

I haven't learned this yet, so just curious, how would 2 be considered to be a complex number?

CalculatorUser  Sep 26, 2019
 #3
avatar+6045 
+1

All reals are also complex numbers.

 

A complex number need not have an imaginary part.

Rom  Sep 26, 2019

30 Online Users

avatar
avatar
avatar