# Thread: Find the complex number z such that...

1. ## Find the complex number z such that...

How do I solve this type of problem?

Find the complex number z such that (−5+i)z+(−4+i)z=−2−i

the answer must be in the form z = ___ + ___i

Thanks in advance for any help!

2. Originally Posted by melissa727
Find the complex number z such that (−5+i)z+(−4+i)z=−2−i
the answer must be in the form z = ___ + ___i
It is very hard to read that notation.

Is it $\displaystyle (-5+i)z+(-4+i)z=-2-i?$

If so note that is $\displaystyle (-9+2i)z=-2-i$ .

If not then try to correct the notation.

3. That is almost the correct notation
except the second z has a bar over it
This is my first time on this site an I don't know how to make my notation like yours... or how to put a bar over my z

4. To see the code for LaTex, just click on the LaTex itself.

For example, to see the code for $\displaystyle (-5+ i)z+ (-4+ i)\overline{z}= -2- i$, click on that formula.

To solve the problem write z as a+ bi so that $\displaystyle \overline{z}= a- bi$. Replace z and $\displaystyle \overline{z}$ by those in the equation and do the arithmetic. Setting the real part on the left equal to the real part on the right and the imaginary part on the left equal to the imaginary part on the right will give you two equations to solve for a and b.