Solver ARITHMETIC on Complex Numbers

Source code of 'ARITHMETIC on Complex Numbers'

This Solver (ARITHMETIC on Complex Numbers) was created by by ichudov(499)

: View Source, Show, Put on YOUR site
About ichudov: I am not a paid tutor, I am the owner of this web site.

==section input

Evaluate *[input a_real=2] + *[input a_imag=1]i *[choice operation + - * /] *[input b_real=2] + *[input b_imag=1]i.

==section solution
perl
my $result;

sub signed {
 my $a = shift @_;
 return $a if $a < 0;
 $a =~ s/^(\d)/+$1/;
 return $a;
}
 if ( $operation eq '+' ) { 
 $r_real = $a_real + $b_real; 
 $r_imag = $a_imag + $b_imag; 
 print "$r_real ".signed( $r_imag)."i. 
Solution:Addition of two complex numbers <CODE>a + bi</CODE> 
 and <CODE>c+di</CODE> is done according to formula:

<CENTER>(a + bi) + (c+di) = (a+c) + (b+d)i.</CENTER> 
 
In our case, {{{
 ($a_real + $a_imag*i) + ($b_real + $b_imag*i) 
 = ($a_real+$b_real) + ($a_imag+$b_imag)*i = $r_real+$r_imag*i}}}.";
 } elsif ( $operation eq '-' ) { 
 $r_real = $a_real - $b_real; 
 $r_imag = $a_imag - $b_imag; 
 print "
Solution:Subtraction of two complex numbers <CODE>a + bi</CODE> 
 and <CODE>c+di</CODE> is done according to formula: 
<CENTER><CODE>(a + bi) - (c+di) = (a+c) - (b+d)i.</CODE></center> 
 
In our case, {{{($a_real + $a_imag*i) - ($b_real + $b_imag*i) 
 = ($a_real - $b_real) + ($a_imag-$b_imag)i 
 = $r_real + $r_imag*i}}}"; 
 } elsif ( $operation eq '*' ) { 
 $r_real = $a_real * $b_real - $a_imag * $b_imag; 
 $r_imag = $a_real * $b_imag + $a_imag * $b_real; 
 print "
Solution:Multiplication of two complex numbers <CODE>a + bi</CODE> 
 and <CODE>c+di</CODE> is done according to formula: 
<center><CODE>(a + bi) * (c+di) = (ac-bd) + (ad+bc)i.</center> 
 
In our case, {{{($a_real + $a_imag*i) * ($b_real + $b_imag*i) 
 = ($a_real*$b_real - $a_imag*$b_imag) + ($a_real*$b_imag + $a_imag*$b_real)*i 
 = $r_real + $r_imag*i}}}"; 
 } elsif ( $operation eq '/' ) { 
 my $d = $b_real*$b_real + $b_imag*$b_imag; 
 $r_real = ($b_imag*$a_imag+$b_real*$a_real)/$d; 
 $r_imag = ($b_real*$a_imag-$b_imag*$a_real)/$d; 
 print "
Solution:Division of two complex numbers <CODE>a + bi</CODE> 
 and <CODE>c+di</CODE> is done according to formula:
 {{{(a + bi) / (c+di) = (db+ca)/(c^2+d^2) + i*((cb-da)/(c^2+d^2))}}} 
 
In our case, {{{($a_real + $a_imag*i) / ($b_real + $b_imag*i) = $r_real + $r_imag*i}}}"; 
 }

==section output
r_real
r_imag

==section check
 z=1

==section practice
perl
  $a_real = randint( -5, 5 );
  $a_imag = randint( -5, 5 );
  $b_real = randint( -5, 5 );
  $b_imag = randint( -5, 5 );