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PIT_PIT [208]
3 years ago
13

Write the expression in standard form. five divided by quantity three minus fifteen i.

Mathematics
1 answer:
marta [7]3 years ago
7 0
The answer is \frac{5}{78}+ \frac{25}{78}i

\frac{5}{3-15i} =\frac{5}{3-15i}* \frac{3+15i}{3+15i} = \frac{5(3+15i)}{(3-15i)(3+15i)}  \\  \\ 
a^{2} -b^{2} =(a+b)(a-b) \\  \\ 4 + 
 \frac{5(3+15i)}{(3-15i)(3+15i)} =  \frac{15+75i}{ 3^{2}-(15i)^{2} } = \frac{15+75i}{9-15^{2}i^{2}}  \\  \\  i^{2}=-1 \\  \\ 
 \frac{15+75i}{9-15^{2}i^{2}} =\frac{15+75i}{9-225*(-1)} =\frac{15+75i}{9+225} = \frac{15+75i}{234} = \frac{3*5+3*25i}{3*78} = \frac{3(5+25i)}{3*78} = \\  \\ 
= \frac{5+25i}{78}= \frac{5}{78}+ \frac{25i}{78}   =\frac{5}{78}+ \frac{25}{78}i
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