LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= x:=4+2*I;

LCYiIiUiIiIqJiIiI0YkXiNGJEYkRiQ=

y:=3-I;

LCYiIiQiIiJeI0YkISIi

z:=7-3*I;

LCYiIigiIiIqJiIiJEYkXiNGJEYkISIi

cz:=conjugate(z);

LCYiIigiIiIqJiIiJEYkXiNGJEYkRiQ=

x*y;

LCYiIzkiIiIqJiIiI0YkXiNGJEYkRiQ=

x/y;

LCYiIiJGI14jRiNGIw==

x*cz+y;

LCYiI0QiIiIqJkYjRiReI0YkRiRGJA==

op(1,convert(x*cz+y,polar));

LCQqJiIjRCIiIikiIiMjRiVGJ0YlRiU=

op(2,convert(x*cz+y,polar));

LCQqJiMiIiIiIiVGJUkjUGlHJSpwcm90ZWN0ZWRHRiVGJQ==

convert(x*cz+y,polar);

LUkmcG9sYXJHSShfc3lzbGliRzYiNiQsJComIiNEIiIiKSIiIyNGKkYsRipGKiwkKiYjRioiIiVGKkkjUGlHJSpwcm90ZWN0ZWRHRipGKg==

x:=a+b*I;

LCZJImFHNiIiIiIqJl4jRiVGJUkiYkdGJEYlRiU=

y:=c+d*I;

LCZJImNHNiIiIiIqJl4jRiVGJUkiZEdGJEYlRiU=

x+y;

LCpJImFHNiIiIiIqJl4jRiVGJUkiYkdGJEYlRiVJImNHRiRGJSomRidGJUkiZEdGJEYlRiU=

x*y;

KiYsJkkiYUc2IiIiIiomXiNGJkYmSSJiR0YlRiZGJkYmLCZJImNHRiVGJiomRihGJkkiZEdGJUYmRiZGJg==

expand(x*y);

LCoqJkkiYUc2IiIiIkkiY0dGJUYmRiYqKF4jRiZGJkYkRiZJImRHRiVGJkYmKihGKUYmSSJiR0YlRiZGJ0YmRiYqJkYsRiZGKkYmISIi

x-y;

LCpJImFHNiIiIiIqJl4jRiVGJUkiYkdGJEYlRiVJImNHRiQhIiIqJiwkRidGJUYlSSJkR0YkRiVGKg==

x/y;

KiYsJkkiYUc2IiIiIiomXiNGJkYmSSJiR0YlRiZGJkYmLCZJImNHRiVGJiomRihGJkkiZEdGJUYmRiYhIiI=

expand(x/y);

LCYqJiwmSSJjRzYiIiIiKiZeI0YnRidJImRHRiZGJ0YnISIiSSJhR0YmRidGJyooRilGJ0YkRitJImJHRiZGJ0Yn

assume(theta,real); assume(phi,real); simplify(r*(cos(theta)+I*sin(theta))/R*(cos(phi)+I*sin(phi)),trig);

KihJInJHNiIiIiJJIlJHRiQhIiIsKiomLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJ3RoZXRhfGlyR0YkRiUtRis2I0klcGhpfGlyR0YkRiVGJSooXiNGJUYlRipGJS1JJHNpbkdGLEYyRiVGJSooRjVGJS1GN0YvRiVGMUYlRiUqJkY5RiVGNkYlRidGJQ==

combine(evalc(%));

KiYsJiomSSJyRzYiIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJkkndGhldGF8aXJHRiZGJ0klcGhpfGlyR0YmRidGJ0YnKiheI0YnRidGJUYnLUkkc2luR0YqRi1GJ0YnRidJIlJHRiYhIiI=

exp(3*Pi*I/2);

LCReIyIiIiEiIg==

S:=(m,n)-> sum( exp(2*Pi*(n-m)*k*I/10),k=0..9)/10;

Zio2JEkibUc2IkkibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQtSSRzdW1HRiU2JC1JJGV4cEdGJTYjKipeIyMiIiIiIiZGNEkjUGlHJSpwcm90ZWN0ZWRHRjQsJjklRjQ5JCEiIkY0SSJrR0YlRjQvRjw7IiIhIiIqI0Y0IiM1RiVGJUYl

S(m,5);

LDYjIiIiIiM1RiQtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyooXiMjRiQiIiZGJEkjUGlHRilGJCwmRjBGJEkibUdGKyEiIkYkRiMtRic2IyooXiMjIiIjRjBGJEYxRiRGMkYkRiMtRic2IyooXiMjIiIkRjBGJEYxRiRGMkYkRiMtRic2IyooXiMjIiIlRjBGJEYxRiRGMkYkRiMtRic2IyooXiNGJEYkRjFGJEYyRiRGIy1GJzYjKiheIyMiIidGMEYkRjFGJEYyRiRGIy1GJzYjKiheIyMiIihGMEYkRjFGJEYyRiRGIy1GJzYjKiheIyMiIilGMEYkRjFGJEYyRiRGIy1GJzYjKiheIyMiIipGMEYkRjFGJEYyRiRGIw==

S(0,0);

IiIi

S(1,1);

IiIi

S(2,2);

IiIi

S(3,3);

IiIi

S(4,4);

IiIi