Find the first three output values of the fractal generating function f(z) = z2 + 2 + i. a. 2 + i, 5 + 5i, –2595 + 205i b. 2 + i, 2 + 51i, –2595 + 205i c. 2 + i, 5 + 5i, 2 + 51i d. 5 + 5i, 2 + 51i, –2595 + 205i

A fractal generating function is given by

 f(z) = Z² + 2 +i

→f(0) = 0² + 2 + i

= 2 + i

→f(2+i) = (2+i)² + 2 + i                      →Use identity (a+b)² = a² + b² + 2 a b

                                                             and i² = -1

        = 4 + 4 i -1 + 2 + i

        = 5 + 5 i

Now→, f(5 + 5 i) = (5 + 5 i)² + 2 + i         →Use identity (a+b)² = a² + b² + 2 ab

                                                             and i² = -1

                         = 25 - 25 + 50 i + 2 + i

                          = 51 i + 2

→So,f(0)=2 + i,  f(2 +i) = f(5 + 5 i) = 2 + 51 i

→Option C, 2 + i, 5 + 5 i, 2 + 51 i are the first three output of fractal generating function f(z) = z² + 2 + i.

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9