The discussion centers on solving simultaneous equations involving complex numbers, specifically the equations 2w + iz = 3 and (3 - i)w - z = 1 + 3i. The user attempts to isolate the variable w but arrives at an incorrect conclusion, stating w = -i/6 - 1/6 instead of the correct answer, w = i/6 + 1/6. The confusion arises from the manipulation of the equations and the calculation of -1/(i-1), which is critical for finding the correct value of w.
PREREQUISITESStudents studying complex analysis, mathematicians solving algebraic equations, and anyone interested in mastering the manipulation of complex numbers in mathematical contexts.
kukumaluboy said:Homework Statement
1) 2w+iz = 3; 2) (3-i)w - z = 1 +3i
2wi - z = 3i; 3w - iw - z = 1 + 3i
Substract (2) from (1):
2wi - z - (3w-iw-z) = 3i - (1+3i)
2wi -3w +iw = -1
3iw - 3w = -1
3w(i-1) = -1
3w = -1/(i-1) = -0.5i - 0.5
w = -i/6 - 1/6
But the answer is i/6 + 1/6 for W