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Naily [24]
1 year ago
11

Perform the indicated operation and express the result as a simplified complex number. I need help with 35

Mathematics
1 answer:
skelet666 [1.2K]1 year ago
3 0

Given:-

\frac{3+4i}{2-i}

To find:-

The simplified form.

At first we take conjucate and multiply below and above.

The conjucate is,

2+i

So now we multiply. we get,

\frac{3+4i}{2-i}\times\frac{2+i}{2+i}

Now we simplify. so we get,

\frac{3+4i}{2-i}\times\frac{2+i}{2+i}=\frac{6+3i+8i+4(i)^2}{2^2-i^2}

We know the value of,

i^2=-1

Substituting the value -1. we get,

\begin{gathered} \frac{6+3i+8i+4(i)^2}{2^2-i^2}=\frac{6+3i+8i+4(-1)_{}^{}}{2^2-(-1)^{}} \\ \text{                               =}\frac{6-4+11i}{2+1} \\ \text{                              =}\frac{2+11i}{3} \end{gathered}

So now we split the term to bring it into the form a+ib. so we get,

\frac{2+11i}{3}=\frac{2}{3}+i\frac{11}{3}

So the required solution is,

\frac{2}{3}+i\frac{11}{3}

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