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[Solved] Write the following complex number in the form x + iy:

 
Complex Numbers
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June 15, 2021 2:37 pm
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Write the following complex number in the form x+iy:

\frac{(2+3i)(-1+2i)}{2+i}-\frac{1-i}{1-2i}.

 

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June 15, 2021 2:37 pm
Topic starter
Staff 
(@armor)
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317 Posts
156 153 0

\small \frac{(2+3i)(-1+2i)}{2+i}-\frac{1-i}{1-2i}=\frac{(2+3i)(2+i)i}{2+i}-\frac{1-i}{1-2i}*\frac{1+2i}{1+2i}

\small =(2+3i)i-\frac{1}{5}(1+2+i\left \{ -1+2 \right \})=-3+2i-\frac{3}{4}-\frac{1}{5}i=-\frac{18}{5}+\frac{9}{5}i.

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