The data in this problem are a set of 6 integers a through f, which you see belo

Question

The data in this problem are a set of 6 integers a through f, which you see below. Use a different set of [a b c d e f] for you submission;

a b c d e f

3 7 9 8 2 9

For the purposes of turning in your answer, define "m_1" to be the "a" that you use, "m_2" to be b, "m_3" to be c, "m_4" to be e, and "m_6" to be f.

Symbols like "ab" denote "a times b" in these problem. (not the decimal ab.0.)

1. Compute the (real and imaginary parts of the) principal value of the seventh root of

(abc + ide/f) to 3 decimal places (accurate to 10-3). Call the real part "m7", and the imaginary part "m8" (for the submission format on the last page). Do not include the i in m8.

Compute the other 6 seventh roots of (abc + ide/f) to 3 decimal places, listed counterclockwise around the origin in the complex plane.

Let m9 be the real part of the second root; let m10 be the imaginary part of the second root.

Let m11 be the real part of the third root; let m12 be the imaginary part of the third root.

And so on; m20 will be the imaginary part of the seventh root.

2. What, to 3 decimal places, is the principal value of [ab/f - ie](b - id)/9 (real and imaginary parts)? Call the real part "m21", and the imaginary part "m22". Simply ask MATLAB for (a*b/f - i*e)^((b - i*d)/9) .

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NOTE : The answer is graded automatically by a MATLAB program. It is important that you submit your answers in the correct format.check your submission before you send it to me. As a check before you submit, open MATLAB, copy/paste your data in (including the brackets), and hit "Enter"; if it is in the proper format, MATLAB will neatly display the data as a 22-by-1 matrix. (Count the lines to be sure.)

NOTE: See Example on how should be done; see below

M=[1.0000

2.0000

3.0000

4.0000

5.0000

6.0000

1.3736

0.1164

1.2351

-3.3925

-3.0812

0.3644

-0.6362

11.2587

4.0550

-3.4148

3.5181

-0.2488

-0.8514

1.5821

-1.0000

2.2222]

Explanation / Answer

function m=matrix(a,b,c,d,e,f)

m(1)=a;

m(2)=b;

m(3)=c;

m(4)=d;

m(5)=e;

m(6)=f;

m(7)=real((a*b*c+1i*d*e/f)^(1/7));

m(8)=imag((a*b*c+1i*d*e/f)^(1/7));

theta=atan(m(8)/m(7));

r=abs((a*b*c+1i*d*e/f)^(1/7));

for i=1:6

x=r*(cos(theta+2*pi*i/7)+1i*sin(theta+2*pi*i/7));

m(2*(4+i)-1)=real(x);

m(2*(4+i))=imag(x);

end

y=(a*b/f-1i*e)^((b-1i*d)/9);

m(21)=real(y);

m(22)=imag(y);

m=m.';

end

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