z-2iz-3-3i-geometrical-representation-is-

Question Number 146041 by alcohol last updated on 10/Jul/21

z^{'} = 2 i z + (3 - 3 i)

g e o m e t r i c a l r e p r e s e n t a t i o n i s ?

Answered by ajfour last updated on 10/Jul/21

\frac{d x}{d t} + i \frac{d y}{d t} = 2 i (x + i y) + 3 (1 - i)

\Rightarrow \frac{d x}{d t} = 3 - 2 y

\frac{d y}{d t} = 2 x - 3

\frac{d x}{3 - 2 y} = \frac{d y}{2 x - 3}

\int (2 x - 3) d x + \int (2 y - 3) d y = c

x^{2} - 3 x + y^{2} - 3 y = c

{(x - \frac{3}{2})}^{2} + {(y - \frac{3}{2})}^{2} = c + \frac{9}{2}

Commented by alcohol last updated on 10/Jul/21

z^{'} i s t h e i m a g e o f z

Commented by mr W last updated on 10/Jul/21

h o w i s y o u r i m a g e o f z d e f i n e d ?

Commented by alcohol last updated on 10/Jul/21

i t i s a t r a n s f o r m a t i o n

(s i m i l i t u d e) a n d a m a s k e d t o g i v e t h e

g e o m e t r i c a l i n t e r p r e t i o n

Answered by Ar Brandon last updated on 10/Jul/21

Soient A (a) et B (a) deux points distinct et A^{'} (a^{'}), B^{'} (b^{'})

leurs images par s, alors on a;

a^{'} = 2 ia + (3 - 3 i), b^{'} = 2 ib + (3 - 3 i)

a^{'} - b^{'} = 2 i (a - b) \Rightarrow∣ a^{'} - b^{'} ∣= 2 ∣ a - b ∣ . Par suite A^{'} B^{'} = 2 AB

s est une similitude de rapport 2 .

Answered by physicstutes last updated on 11/Jul/21

let the image of a be a^{'} and the image of b be b^{'}

then, a^{'} = 2 i a + (3 - 3 i) \dots . . (i)

b^{'} = 2 i b + (3 - 3 i) \dots \dots (i i)

(i i) - (i) \Rightarrow b^{'} - a^{'} = 2 i (b - a)

\Rightarrow ∣ b^{'} - a^{'} ∣ = 2 ∣ b - a ∣

So we say your transformation call it f is a similitude of radius

2, since similitudes are enlargments . Then Geometrically

you will inteprete that f is an enlargment scale factor 2

followed by a translation about the vector (\begin{matrix} 3 \\ - 3 \end{matrix})