3dimensions thnx da
if α, β, γ, δ are four complex numbers such that γ/δ is real and αδ - βγ ≠0, then z = (α+βt)/(γ+δt), tεR represents a
a) circle
b)parabola
c)ellipse
d) straight line
e) hyperbola.
Please answer this question....
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2 Answers
1now,
let γ/δ = k (real)
so
Z={1/(k+t)} ((α/δ)+t(β/δ))
Z = {1/(k+t)} (k(α/γ)+t(β/δ))
now ,
let α/γ = z1 & β/δ = z2
it is given that z1 ≠z2
Z = {1/(k+t)} (kz1+tz2)
Z = {1/(k+t)} ((k+t)z1+t(z2-z1))
Z = z1+{t/(k+t)}(z2-z1)
let λ = t/(k+t) (real)
Z = z1+λ(z2-z1)
now this represents an equation of a straight line passing through z1 & parallel to (z2-z1)
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