Let the given complex number
z = x + ix =
We have to find the standard form of complex number.
Solution:
∴ x + iy =
Rationalising numerator part of complex number, we get
x + iy =
⇒ x + iy =
Using the algebraic identity:
(a + b)(a - b) = -
⇒ x + iy =
⇒ x + iy = [ ∵
]
⇒ x + iy =
⇒ x + iy =
⇒ x + iy =
⇒ x + iy = 1 - i
Thus, the given complex number in standard form as "1 - i".
The scale factor that was applied to figure A to produce figure B is: 11/3 = 3.67.
<h3>How to Find the Scale Factor of a Dilation?</h3>The ratio of the corresponding dimensions of the image to the preimage gives the scale factor of any dilation.
That is:
Scale factor = dimension of image (new figure) / corresponding dimension of pre-image (original figure).
The scale factor that was applied to figure A to produce figure B = dimension of figure B / corresponding dimension of figure A.
A dimension of figure B = 33
Corresponding dimension of figure A = 9
Therefore, we would find the scale factor as shown below:
The scale factor that was applied to figure A to produce figure B = 33/9
= 11/3 = 3.67
Therefore, the scale factor that was applied to figure A to produce figure B is: 11/3 = 3.67.
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