Question-138829

Question Number 138829 by 676597498 last updated on 18/Apr/21

Answered by physicstutes last updated on 19/Apr/21

T : z \to ω \Rightarrow ω = 3 z + 2 - 5 i

(a) This transformation is an enlargment of scale factor 3 followed by

a translation of (2, - 5) .

(b) For invariant point, f (z) = z

\Rightarrow z = 3 z + 2 - 5 i \Rightarrow z = - 1 + \frac{5}{2} i

(c) \bar{a} = 3 a + 2 - 5 i \dots . . (i)

\bar{b} = 3 b + 2 - 5 i \dots . . (i i)

(i i) - (i) \Rightarrow ∣ \bar{b} - \bar{a} ∣ = 3 ∣ b - a ∣ \Rightarrow T is a simultitude of radius 3 .

(d) if z is a circle centered O and radius 2 then ∣ z ∣ = 2

∣ ω - (2 - 5 i) ∣= 6, then ω will be a circle centred (2, - 5) and radius 6 .

since T is an enlargment (scale factor 3) and a translation by (2, - 5) .