Solution Found!
Detennine a pair of complex numbers z == a + bi and w == c + di giving a solution of
Chapter 32, Problem 32.7(choose chapter or problem)
Detennine a pair of complex numbers \(z=a+b i\) and \(w=c+d i\) giving a solution of the system
\(\begin{aligned}
3 z-2 w & =-i \\
i z+2 i w & =-5 .
\end{aligned}\)
(The usual methods of solving systems of equations over \(\mathbb{R}\) also work over \(\mathbb{C}\). Why?)
Questions & Answers
QUESTION:
Detennine a pair of complex numbers \(z=a+b i\) and \(w=c+d i\) giving a solution of the system
\(\begin{aligned}
3 z-2 w & =-i \\
i z+2 i w & =-5 .
\end{aligned}\)
(The usual methods of solving systems of equations over \(\mathbb{R}\) also work over \(\mathbb{C}\). Why?)
ANSWER:Step 1 of 6
Multiply Equation (1) by i and add the resulting equation to Equation (2).
Now, Multiply Equation (1) by
\(\begin{array}{l}
3 i z-2 i w=-i^{2} \\
i z+2 i w=-5 \\
\hline 4 i z=-i^{2}-5
\end{array}\)