((3-i)/(5+2i))+(7-4i)

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Solution for ((3-i)/(5+2i))+(7-4i) equation: 


D( i )

2*i+5 = 0

2*i+5 = 0

2*i+5 = 0

2*i+5 = 0 // - 5

2*i = -5 // : 2

i = -5/2

i in (-oo:-5/2) U (-5/2:+oo)

(3-i)/(2*i+5)-(4*i)+7 = 0

(3-i)/(2*i+5)-4*i+7 = 0

(3-i)/(2*i+5)+(-4*i*(2*i+5))/(2*i+5)+(7*(2*i+5))/(2*i+5) = 0

7*(2*i+5)-4*i*(2*i+5)-i+3 = 0

14*i-8*i^2-21*i+3+35 = 0

38-8*i^2-7*i = 0

38-8*i^2-7*i = 0

38-8*i^2-7*i = 0

DELTA = (-7)^2-(-8*4*38)

DELTA = 1265

DELTA > 0

i = (1265^(1/2)+7)/(-8*2) or i = (7-1265^(1/2))/(-8*2)

i = (1265^(1/2)+7)/(-16) or i = (7-1265^(1/2))/(-16)

(i-((1265^(1/2)+7)/(-16)))*(i-((7-1265^(1/2))/(-16))) = 0

((i-((1265^(1/2)+7)/(-16)))*(i-((7-1265^(1/2))/(-16))))/(2*i+5) = 0

((i-((1265^(1/2)+7)/(-16)))*(i-((7-1265^(1/2))/(-16))))/(2*i+5) = 0 // * 2*i+5

(i-((1265^(1/2)+7)/(-16)))*(i-((7-1265^(1/2))/(-16))) = 0

( i-((1265^(1/2)+7)/(-16)) )

i-((1265^(1/2)+7)/(-16)) = 0 // + (1265^(1/2)+7)/(-16)

i = (1265^(1/2)+7)/(-16)

( i-((7-1265^(1/2))/(-16)) )

i-((7-1265^(1/2))/(-16)) = 0 // + (7-1265^(1/2))/(-16)

i = (7-1265^(1/2))/(-16)

i in { (1265^(1/2)+7)/(-16), (7-1265^(1/2))/(-16) }

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