Complex Numbers, Multiply by Conjugate?

• September 21st 2009, 11:40 AM
DoubtImReal
Complex Numbers, Multiply by Conjugate?
Taking Further Maths at secondary school here in England, and I'm struggling with some of the concepts to do with complex numbers. One question I have for homework right now is the following:

(1+j)z=3+j

I am pretty sure I can do the question in general as I have notes, but have no idea how to start it off. Thinking it might involve multiplying by the conjugate, but can't get to that stage. Any help would be appreciated.
• September 21st 2009, 11:45 AM
Plato
Quote:

Originally Posted by DoubtImReal
Taking Further Maths at secondary school here in England, and I'm struggling with some of the concepts to do with complex numbers. One question I have for homework right now is the following:

(1+j)z=3+j.

$\begin{gathered}
\left( {1 + i} \right)z = \left( {3 + i} \right) \hfill \\
\overline {\left( {1 + i} \right)} \left( {1 + i} \right)z = \overline {\left( {1 + i} \right)} \left( {3 + i} \right) \hfill \\
2z = \left( {1 - i} \right)\left( {3 + i} \right) \hfill \\
\end{gathered}$
• September 21st 2009, 11:45 AM
Matt Westwood
Quote:

Originally Posted by DoubtImReal
Taking Further Maths at secondary school here in England, and I'm struggling with some of the concepts to do with complex numbers. One question I have for homework right now is the following:

(1+j)z=3+j

I am pretty sure I can do the question in general as I have notes, but have no idea how to start it off. Thinking it might involve multiplying by the conjugate, but can't get to that stage. Any help would be appreciated.

Divide by $1+j$, you get:

$z = \frac {3+j} {1+j}$

and then indeed you multiply top and bottom of RHS by the conjugate of $1+j$.

I'll leave you to finish off.

I did further maths at an English secondary school myself, some (harumphty humph) years ago. Respect.