Question

Simplify:7/1+4i

Answer 1

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

Answer 2

yea

Answer 3

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

Answer 4

no

Answer 5

(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?

Answer 6

got it

Answer 7

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

Answer 8

7+28i

Answer 9

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