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Lilit [14]
3 years ago
13

Find the first three iterates of the function f(z) = z2 + c with a value of c = 2 - 3i and an initial value of z0 = 1 + 2i.

Mathematics
1 answer:
Artist 52 [7]3 years ago
3 0

Answer:

C

Step-by-step explanation:

We have: (I rewrote the function)

f(z_n)={z_{n-1}} ^2+c

Given that:

\displaystyle c=2-3i \text{ and } z_0 = 1 + 2 i

The first iterate will be:

\displaystyle \begin{aligned} f(z_1)&=(z_0)^2+c \\ &=(1+2i)^2+(2-3i) \\ &= (1+4i+4i^2)+(2-3i) \\ &=1+4i-4+2-3i \\ &=-1+i \end{aligned}

The second iterate will be:

\begin{aligned}f(z_2) &=(z_1)^2+c\\ &=(-1+i)^2+(2-3i) \\&= (1-2i+i^2)+(2-3i) \\&=1-2i-1+2-3i \\&=2-5i \end{aligned}

And the third iterate will be:

\begin{aligned} f(z_3)&=(z_2)^2+c\\ &=(2-5i)^2+(2-3i) \\ &=(4-20i+25i^2)+(2-3i) \\ &=4-20i-25+2-3i \\ &=-19-23i \end{aligned}

Hence, our answer is C.

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Answer:

3

Step-by-step explanation:

Given that:

Integers : x, x + 1, x + 2

6x - 2(x + 1) = (x+2) + 5

6x - 2x - 2 = x + 2 + 5

4x - 2 = x + 7

4x - x = 7 + 2

3x = 9

x = 9/3

x = 3

First integer = x = 3

2nd integer = x + 1 = 3+1 = 4

3rd Integer = x + 1 + 1 = 3 + 2 = 5

7 0
3 years ago
Is y=150x proportional?
daser333 [38]

Answer:

yes

Step-by-step explanation:

A proportional equation is of the form

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y = 150x is proportional

5 0
3 years ago
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Cookies are sold singly or in packages of 3 or 9. With this packaging, how many ways can you buy 18 cookies?
tresset_1 [31]
I believe 5 different ways. The options being two packs of 9-one pack of 9 and 3 packs of 3- 1 pack of 9, 2 packs of 3 and 3 singles- one pack of 9, one pack of 3, and 6 singles- and then one pack of 9 and 9 singles.
Hope this helped!

8 0
3 years ago
A motorcyclist leaves City A and rides at a constant speed towards City B, which is 225 km away. After 1.5 hours, the motorcycli
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Answer:

50 km/hr

Step-by-step explanation:

OK, this is how I solved this problem.

Let r = original rate of speed

     t = time after the stop to finish the trip

Time for trip without stopping is 225/r

(1)     1.5 + .5 + t = 225/r      This is a time equation

(2)    1.5r + t(r + 10) = 225     This is a distance equation

(1)       2 + t = 225/r            (2)      1.5r + tr + 10t = 225

         2r + tr = 225

                tr = 225 - 2r                 1.5r + 225 - 2r + 10(225/r - 2) = 225

                t = 225/r - 2

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                                                     -5r^2 + 2250r + 22500 - 200r = 2250r

                                                       5r^2 + 200r - 22500 = 0

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The rate cannot be negative, so the original speed 50 km/hr

This not an easy problem and I hope you were able to follow my work

5 0
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Answer:

You already did the question.

Step-by-step explanation:

What's there to simplify?

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