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Mathematics

OpenStudy (anonymous):

Simplify:7/1+4i

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OpenStudy (lgbasallote):

\[\large \frac{7}{1 + 4i}\] that right?

OpenStudy (anonymous):

yea

OpenStudy (lgbasallote):

do you know the conjugate of \(1 + 4i\)?

OpenStudy (anonymous):

no

OpenStudy (lgbasallote):

(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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OpenStudy (anonymous):

got it

OpenStudy (lgbasallote):

now multiply \(1-4i\) to numerator and denominator...note: DO NOT cancel

OpenStudy (anonymous):

7+28i

OpenStudy (anonymous):

\[\frac{ 7 }{1+4i } *\frac{1-4i }{1-4i }\\ \frac{ 7(1-4i ) }{1-(4i)^2 }\\\\ \frac{ 7-28i }{1-16i^2 }\\\\ \frac{ 7-28i }{1-16(-1) }\\\\ \frac{ 7-28i }{1+16 }\\\\ \frac{ 7-28i }{17 } \]

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