You are here:

- Home
- Science
- Mathematics
- Number Theory
- Simultaneous equations having complex numbers.

Advertisement

Dear Prof Vijilant

Can Simultaneous equations have complex numbers and can be solved?

Example

(2+3i)x+(4-2i)y=2

(3+2i)x+(2-3i)y=1

Thanks

Prashant

Certainly. We just follow the usual procedure. In this case multiply (1) by 2-3i and (2) by 4-2i to get

11x + (2 - 16i)y = 4 - 6i

(16 + 2i)x + (2 - 16i)y = 4 - 2i

Subtract: (5 + 2i)x = 4i

x = 4i/(5+2i) = 4i(5 - 2i)/(5^2 + 2^2) = (8 + 20i)/29

Substitute in (1) (2 + 3i)(8 + 20i)/29 + (4 - 2i)y = 2

(-44 + 64i)/29 + (4 - 2i)y = 2

-44 + 64i +29(4 -2i)y = 58

29(4 - 2i)y = 102 -64i

y = (102 - 64i)/(29(4 - 2i)) = (102 -64i)(4 + 2i)/(29*20) = (536 -52i)/(29*20) = (134 -13i)/145

Best wishes

vijilant

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | Dear Prof Vijilant Thanks. Prashant |

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Teacher of math for 53 years**Organizations**

AQA
Doncaster Bridge Club
Danum Strings Orchestra
Doncaster Conservative Club
Danum Strings Orchestra
Simply Voices Choir Doncaster
TNS mystery shopping
St Paul's Music Group Cantley
**Publications**

Journal of mathematics and its applications
M500 magazine**Education/Credentials**

BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)**Awards and Honors**

State Scholarship 1955
Highest Score in Yorkshire on OU course MST209 £50 prize
First class honours in OU BA Mathematics**Past/Present Clients**

I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things.
One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.