Solutions Manual for A MATLAB Companion to Complex Variables.

1 Solutions Manual for A MATLAB Companion to Complex Variables.Chapter 1

SECTION 1.1

SEC 1.1

Problem 1 format short solution='PROBLEM 1' a=(3-4i)/(1+2i)+2i b=(2+i)/(3+5i)-1-i/2 c=(1+2*i/3)^3-i/(3-4i)^3 d=(1+2/(3i))^11 e=(2i/(3+4i)+conj(1/(5 -4i)))^5

OUTPUT FROM THE ABOVE PROGRAM

solution =

PROBLEM 1

a = -1 b = -0.6765 - 0.7059i c = -0.3305 + 1.7112i d = 7.4284 - 1.3889i e = 0.0003 + 0.0216i solution = A MatLab® Companion to Complex Variables, 1e A David Wunsch (Solutions Manual All Chapters, 100% Original Verified, A+ Grade) 1 / 4

2

solution='PROBLEM 2' %note that (1+i)^2=2i and (2i)^18= -2^18 since i raised to an even %integer %is plus or minus one;the minus sign holds if the integer not divisible %by4

%so, without matlab, the final answer is -2^18*(1+i)=-2^18-i2^18= %-262144-i262144 %provided you get 2^18 off a pocket calculator or you can notice that

%2^18=8*32^3

format long (1+i)^37

solution='PROBLEM 3a' %part a sa=0;

for n=0:10

z=(i/2)^n; sa=sa+z; end sa

solution='PROBLEM 3b' %part b sb=(1-(i/2)^11)/(1-i/2)

%EXERCISES SEC 1.1

format short solution='PROBLEM 1' a=(3-4i)/(1+2i)+2i b=(2+i)/(3+5i)-1-i/2 c=(1+2*i/3)^3-i/(3-4i)^3 d=(1+2/(3i))^11 e=(2i/(3+4i)+conj(1/(5 -4i)))^5

PROBLEM 2

Without MATLAB   18

37 36 2 18 18

18

(1 ) (1 ) (1 ) (1 ) (1 ) 2 (1 )

2 (1 ) 262144 262144

i i i i i i i ii

        

     

You can compute 18

2 32*32*32*8 =262144

With MATLAB >> format long

>> (1+i)^37 2 / 4

3

ans =

-2.621440000000000e+05 - 2.621440000000000e+05i

3.

solution='PROBLEM 3' %part a sa=0;

for n=0:10

z=(i/2)^n; sa=sa+z; end sa

solution='PROBLEM 3b' %part b sb=(1-(i/2)^11)/(1-i/2)

3.

PROBLEM 3a %problem 3 section1.1 format long s=1;

for n=1:10

s=s+(i/2)^n; end s

WHOSE OUTPUT IS

sa =

0.79980468750000 + 0.40039062500000i

solution =

PROBLEM 3b

>> format long >> (1-(i/2)^11)/(1-i/2)

ans =

0.799804687500000 + 0.400390625000000i 3 / 4

4

SECTION 1.2

Problem 1.

%PROBLEMS 1 %solution='problem 1' %parta a=(1+i)*(sqrt(3)+i) angle_product=angle(a) angle_first=angle(1+i) angle_second=angle(sqrt(3)+i) angle_sum=angle_first+angle_second %partbb=(1+i)*(-sqrt(3)+i) angle_product=angle(b) angle_first=angle(1+i) angle_second=angle(-sqrt(3)+i) angle_sum=angle_first+angle_second

OUTPUT FROM THE ABOVE PROGRAM

solution =

problem 1

a =

0.73205080756888 + 2.73205080756888i

angle_product =

1.30899693899575

angle_first =

0.78539816339745

angle_second =

0.52359877559830

angle_sum =

1.30899693899575

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