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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
2
i
= -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:
Notes:
The product of two numbers is represented by: (x
i (x
y
+ x
y
).
1
2
2
1
The division of two complex numbers is accomplished by multiplying both
numerator and denominator by the complex conjugate of the denominator,
i.e.,
x
iy
x
1
1
1
x
iy
x
2
2
2
Thus, the inverse function INV (activated with the Y key) is defined as
1
x
iy
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
(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)
iy
x
iy
x
x
1
2
2
1
2
2
iy
x
iy
x
2
2
2
2
1
x
iy
x
2
x
iy
x
iy
x
y
+iy
)(x
+iy
) = (x
x
- y
1
1
2
2
1
2
y
y
x
y
x
y
1
2
i
2
1
1
2
2
2
2
y
x
y
2
2
2
y
i
2
2
2
x
y
Page 4-4
y
) +
1
2
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