Quadratic Equation with Complex Coefficients
Description
By Eddie Shore, December 2011 (Eddie's Math and Calculator Blog)
The following equation solves the quadratic equation:
A × Z2 + B × Z + C = 0
where A, B, C, and Z are complex numbers.
The roots are:
-B ± √(B2 - 4·A·C)
Z = ——————————————————
2A
A = R0 + R1i
B = R2 + R3i
C = R4 + R5i
Root 1 = R6 + R7i
Root 2 = R8 + R9i
Instructions:
- Store the real and imaginary parts of A, B, and C. See the above for the appropriate registers.
- Press f A
- The real part of Root 1 is displayed. Press R/S.
- The imaginary part of Root 1 is displayed. Press R/S.
- The real part of Root 2 is displayed. Press R/S.
- The imaginary part of Root 2 is displayed.
Example 1:
Numbers:
A = 2 + 3i
B = -3 - 4i
C = 2i
Registers:
R0 = 2
R1 = 3
R2 = -3
R3 = -4
R4 = 0
R5 = 2
Root 1 ≈ 0.2578 + 0.3769i
Root 2 ≈ 1.1268 - 0.4538i
Example 2:
Numbers:
A = -4 + 5i
B = 3
C = 2√2 - 3i
Registers:
R0 = -4
R1 = 5
R2 = 3
R3 = 0
R4 = 2√2 (2 [ENTER] [ √ ] [ × ])
R5 = -3
Root 1 ≈ -0.6500 + 0.1165i
Root 2 ≈ 0.9427+ 0.2493i
Program Resources
Labels
Storage Registers
Name |
Description |
|
Name |
Description |
|
0 |
real part of A |
|
5 |
imaginary part of C |
|
1 |
imaginary part of A |
|
6 |
real part of root 1 |
|
2 |
real part of B |
|
7 |
imaginary part root 1 |
|
3 |
imaginary part of B |
|
8 |
real part of root 1 |
|
4 |
real part of C |
|
9 |
imaginary part root 2 |
|
Flags
Program
Line |
Display |
Key Sequence |
|
Line |
Display |
Key Sequence |
|
Line |
Display |
Key Sequence |
|
000 |
|
|
|
018 |
44 9 |
STO 9 |
|
036 |
43 11 |
g x² |
|
001 |
42,21,11 |
f LBL A |
|
019 |
31 |
R/S |
|
037 |
40 |
+ |
|
002 |
43, 4, 8 |
g SF 8 |
|
020 |
42 30 |
f Re↔Im |
|
038 |
11 |
√x̅ |
|
003 |
32 0 |
GSB 0 |
|
021 |
43 32 |
g RTN |
|
039 |
43 32 |
g RTN |
|
004 |
32 1 |
GSB 1 |
|
022 |
42,21, 0 |
f LBL 0 |
|
040 |
42,21, 1 |
f LBL 1 |
|
005 |
44 6 |
STO 6 |
|
023 |
45 0 |
RCL 0 |
|
041 |
45 2 |
RCL 2 |
|
006 |
31 |
R/S |
|
024 |
45 1 |
RCL 1 |
|
042 |
16 |
CHS |
|
007 |
42 30 |
f Re↔Im |
|
025 |
42 25 |
f I |
|
043 |
45 3 |
RCL 3 |
|
008 |
44 7 |
STO 7 |
|
026 |
45 4 |
RCL 4 |
|
044 |
16 |
CHS |
|
009 |
31 |
R/S |
|
027 |
45 5 |
RCL 5 |
|
045 |
42 25 |
f I |
|
010 |
32 0 |
GSB 0 |
|
028 |
42 25 |
f I |
|
046 |
40 |
+ |
|
011 |
1 |
1 |
|
029 |
20 |
× |
|
047 |
2 |
2 |
|
012 |
16 |
CHS |
|
030 |
4 |
4 |
|
048 |
10 |
÷ |
|
013 |
20 |
× |
|
031 |
16 |
CHS |
|
049 |
45 0 |
RCL 0 |
|
014 |
32 1 |
GSB 1 |
|
032 |
20 |
× |
|
050 |
45 1 |
RCL 1 |
|
015 |
44 8 |
STO 8 |
|
033 |
45 2 |
RCL 2 |
|
051 |
42 25 |
f I |
|
016 |
31 |
R/S |
|
034 |
45 3 |
RCL 3 |
|
052 |
10 |
÷ |
|
017 |
42 30 |
f Re↔Im |
|
035 |
42 25 |
f I |
|
053 |
43 32 |
g RTN |
|