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sveta [45]
3 years ago
5

Which fraction do you multiply by to simplify 5/ 4 - 3i ?

Mathematics
1 answer:
Rzqust [24]3 years ago
3 0
So I assume
\frac{5}{4-3i}

If so. Let us begin.

\mathrm{Multiply\:by\:the\:conjugate}\:\frac{4+3i}{4+3i} \ \textgreater \  \frac{5\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)} \ \textgreater \  \left(4-3i\right)\left(4+3i\right)

\mathrm{Apply\:complex\:arithmetic\:rule}:\ \left(a+bi\right)\left(a-bi\right)=a^2+b^2
Where\;a=4,\:b=-3 \ \textgreater \  4^2+\left(-3\right)^2 \ \textgreater \  Refine \ \textgreater \  25

\frac{5\left(4+3i\right)}{25} \ \textgreater \  \mathrm{Cancel\:the\:common\:factor:}\:5 \ \textgreater \  \frac{4+3i}{5}

Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number
\frac{4}{5}+\frac{3}{5}i\;is\;our\;answer!

Hope this helps!
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