HP 49g+ - Manual (Page 162)

Page 4-4
Simple operations with complex numbers
Complex numbers can be combined using the four fundamental operations
(
+-*/). The results follow the rules of algebra with the caveat that
i 2 = -1. Operations with complex numbers are similar to those with real
numbers. For example, with the calculator in ALG mode and the CAS set to
Complex, we’ll attempt the following sum: (3+5i) + (6-3i):
Notice that the real parts (3+6) and imaginary parts (5-3) are combined
together and the result given as an ordered pair with real part 9 and
imaginary part 2. Try the following operations on your own:
(5-2i) - (3+4i) = (2,-6)
(3-i) (2-4i) = (2,-14)
(5-2i)/(3+4i) = (0.28,-1.04)
1/(3+4i) = (0.12, -0.16)
Notes:
The product of two numbers is represented by: (x
1
+iy
1
)(x
2
+iy
2
) = (x
1
x
2
- y
1
y
2
) +
i (x
1
y
2
+ x
2
y
1
).
The division of two complex numbers is accomplished by multiplying both
numerator and denominator by the complex conjugate of the denominator,
i.e.,
2
2
2
2
2 1 1 2
2
2
2
2
2 1 2 1
2 2
2 2
2 2
1 1
2 2
1 1
y x
y x y x
i
y x
y y x x
iy x
iy x
iy x
iy x
iy x
iy x
+
−
⋅ +
+
+
=
−
−
⋅
+
+
=
+
+
Thus, the inverse function INV (activated with the Y key) is defined as
2 2 2 2
1 1
y x
y
i
y x
x
iy x
iy x
iy x iy x +
⋅ +
+
=
−
−
⋅
+
=
+
Changing sign of a complex number
Changing the sign of a complex number can be accomplished by using the
\ key, e.g., -(5-3i) = -5 + 3i