Question #$3$: This exercise shows you how to write a MATLAB function that calculates all the

complex$-$valued solutions to the following polynomial:

zn $=$ a

where a is a complex number and n is a positive integer. The solutions are called the nth roots of

the complex number a$.$ For the special case of a $=1,$ the solutions are called the nth roots of unity

$($see Appendix A in the textbook$).$ Hint: Let a $=$ Aej$\backslash$phi be the polar form of a$.$ Then there are

exactly n solutions$/$roots$,$ for k $=0,1,...,$ n $1,$ given by

z $=$ A $1$

n ej $\backslash$phi $+2\backslash$pi k

n $=$

A $1$

n ej $\backslash$phi

n

$|\{$z $\}$

r$1$

$$

ej $2\backslash$pi k

n

$|\{$z $\}$

r$2$

$,$

$($a$)$ Write a MATLAB function r $=$ myroots$($n$,$ a$)$ to find the nth roots of any complex

number by completing the skeleton function provided in myroots.m$.$ The function should

take a and n above and return all of the roots r$.$ Remember to comment your code$\mathrm{.}1$

$($b$)$ After the generation of myroots.m$,$ type in the command window,

$>>$ help myroots

Explain: What purpose does this command serve?

$($c$)$ Use your function to calculate the $7$th roots of j and the $21$st roots of $$j$.$ Check your results!

$1$It is a good practice to print out intermediate results in your function code for debugging when you are developing

your function. However, please turn off printing of all intermediate results $($do you know how?$)$ in the submitted

version of your code to avoid generating extraneously long published report.

$8$