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if(x)=x4-8x3+4x2+4x+39 and f(3+2i)=a+ib then a:b equal

if(x)=x4-8x3+4x2+4x+39 and f(3+2i)=a+ib then a:b equal

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
just put x=3+2i in f(x)
then f(3+2i) = (3+2i)^4 -8(3+2i)^3 + 4(3+2i)^2 + 4(3+2i) + 39
expand the formulas and make it in the form of a+ib
now you will get a=ib= -1+8i
so a:b = -1/8

sorry swarnika when you expand the formula you will get the expression in form of a+ib.
a+ib= 24- 192i
then a:b will come to -1/8

there is another appraoch-
x= 3+2i
now x-3 = 2i
on squaring
x^2-6x+9 = 4i^2
x^2-6x+13=0
now divide f(x) by x^2-6x+13
you get quotient as x^2-2x-21 and remainder as –96x+312
thus f(x)= (x^2-6x+13)(x^2-2x-21) –96x+312
now f(3+2i)= 0* (x^2-2x-21) –96(3+2i)+ 312
thus f(3+2i) = 24 –192i
so a:b = -1/8

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