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Simplify:7/1+4i
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\[\large \frac{7}{1 + 4i}\] that right?
yea
do you know the conjugate of \(1 + 4i\)?
no
(this only applies to binomials)...copy the first term and last term then reverse the sign...in other words \(1 - 4i\) is the conjugate..got it?
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got it
now multiply \(1-4i\) to numerator and denominator...note: DO NOT cancel
7+28i
\[\frac{ 7 }{1+4i } *\frac{1-4i }{1-4i }\\ \frac{ 7(1-4i ) }{1-(4i)^2 }\\\\ \frac{ 7-28i }{1-16i^2 }\\\\ \frac{ 7-28i }{1-16(-1) }\\\\ \frac{ 7-28i }{1+16 }\\\\ \frac{ 7-28i }{17 } \]
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