"Testing polar"

clear

T = polar(1+i)
check(T = 2^(1/2)*exp(1/4*i*pi))
T = polar(-1+i)
check(T = 2^(1/2)*i*exp(1/4*i*pi))
T = polar(-1-i)
check(T = -2^(1/2)*exp(1/4*i*pi))
T = polar(1-i)
check(T = -2^(1/2)*i*exp(1/4*i*pi))

check(infixform(polar(2 + 3 i)) == "13^(1/2) exp(i arctan(3,2))")
check(infixform(polar(2 - 3 i)) == "13^(1/2) exp(-i arctan(3,2))")
check(infixform(polar(-2 + 3 i)) == "13^(1/2) exp(i arctan(3,-2))")
check(infixform(polar(-2 - 3 i)) == "13^(1/2) exp(-i arctan(3,-2))")

check(infixform(polar(1/2)) == "1/2")
check(infixform(polar(-1/2)) == "-1/2")

check(infixform(polar(a)) == "a")
check(infixform(polar(-a)) == "-a")

check(infixform(polar(1/2 a)) == "1/2 a")
check(infixform(polar(-1/2 a)) == "-1/2 a")

check(infixform(polar(a + b)) == "a + b")
check(infixform(polar(i a + i b)) == "i a + i b")

check(infixform(polar(a + i b)) == "(a^2 + b^2)^(1/2) exp(i arctan(b,a))")
