Solving simultaneous equations with imaginary numbers

Question

Consider the following simultaneous equation:

$$\begin{cases} 5z-(3+i)w=7-i\\ (2-i)z+2iw = -1+i \end{cases} $$

What is the simplest way to manipulate one of the equations so that a variable can be eliminated and the equation solved?

w = -16i-10 z= -3i + 14? Are these correct anyone tried them? — , Dec 28 '14 at 23:05

score 6 · Accepted Answer · answered Aug 26 '12 at 06:06

6

You do it the same way you do it over the reals. For example, you could solve the first equation for $z$, $z=(7-i+(3+i)w)/5$, substitute that into the 2nd equation, solve for $w$, then get $z$. Or, multiply the first equation by $2-i$, the second by 5, and subtract to eliminate $z$.

answered Aug 26 '12 at 06:06

Gerry Myerson

179,216

I vote for multiplication by $2-i$ and $5$. – James S. Cook Aug 26 '12 at 06:10
1

In this example, it looks like multiplying the second equation by $2+i$ might be easier. – Mike Aug 26 '12 at 06:33
Mike, yes, for this example, that looks like a very good idea. – Gerry Myerson Aug 26 '12 at 07:08

Solving simultaneous equations with imaginary numbers

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