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\frac{1\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)}
Multiply both numerator and denominator by the complex conjugate of the denominator, 4+3i.
\frac{1\left(4+3i\right)}{4^{2}-3^{2}i^{2}}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{1\left(4+3i\right)}{25}
By definition, i^{2} is -1. Calculate the denominator.
\frac{4+3i}{25}
Multiply 1 and 4+3i to get 4+3i.
\frac{4}{25}+\frac{3}{25}i
Divide 4+3i by 25 to get \frac{4}{25}+\frac{3}{25}i.
Re(\frac{1\left(4+3i\right)}{\left(4-3i\right)\left(4+3i\right)})
Multiply both numerator and denominator of \frac{1}{4-3i} by the complex conjugate of the denominator, 4+3i.
Re(\frac{1\left(4+3i\right)}{4^{2}-3^{2}i^{2}})
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
Re(\frac{1\left(4+3i\right)}{25})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{4+3i}{25})
Multiply 1 and 4+3i to get 4+3i.
Re(\frac{4}{25}+\frac{3}{25}i)
Divide 4+3i by 25 to get \frac{4}{25}+\frac{3}{25}i.
\frac{4}{25}
The real part of \frac{4}{25}+\frac{3}{25}i is \frac{4}{25}.