Mathematics, 19.12.2019 18:31, pingkeara

Will , give five stars, and !

(a) let the function be defined on the complex numbers as prove that the distance between and is a constant multiple of the distance between and , and find the value of this constant.

(b) let the function be defined on the complex numbers as for some real value of . then if is equidistant from and for all , what is equal to?

Answers: 2

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answered: braydenaddison738

(a) √2

(b) 1/2

Step-by-step explanation:

(a) The ratio of distances will be the magnitude of the ratio f(z)/(f(z) -z), so will be ...

|(1+i)z/((1+i)z -z)| = |(1+i)/i| = |1-i| = √(1+1) = √2

___

(b) You want |g(z) -0| = |g(z) -z|, so you have ...

|(a +2i)z -0| = |(a +2i)z -z|

|(a +2i)|·|z| = |a-1 +2i|·|z|

Dividing by the magnitude of z and squaring both sides, we have ...

a^2 +4 = (a-1)^2 +4

0 = -2a +1 . . . . . . subtract a^2+4 and simplify

1/2 = a . . . . . . . . . divide by -2, add 1/2

answered: Guest

Ithink ghe answer to this question is b just trying to others
Find the perimeter of the shape below a- 7.4 units b- 8.9 units c- 11.2 units d- 13.6 units

answered: Guest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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Will , give five stars, and !

(a) let the function be defined on the complex numbers as...