The value of p+q = 403,For the given complex number a+bi and
where p and q are co-primes
F(z)= (a+ib)z⇒this is equidistant from "0" and "z"
Given modulus of complex number (a+ib) = 10 ;
p and q ∈Z
G.C.D of ( p and q)=1
(a+ib)z equidistant from "0" and "z"
![&\Rightarrow|(a+i b) z-z|=|(a+i b) \bar{z}-0|\\&|z(a+i b-1)|=|(a+i b) \bar{z}|\\&[\bar{z}||(a-1)+i b|=| z|(a+i b)|\\&|a-1+i b|=|a+i b|\\&\sqrt{(a-1)^2+b^2}=\sqrt{a^2+b^2}\\&|a+i b|=10 \quad a^2+1-2 a+b^2=x^2+b^2\\&\sqrt{a^2+b^2}=10\\&a=1 / 2\\&a^2+b^2=100\\&b^2=100-\frac{1}{4}\\](https://tex.z-dn.net/?f=%26%5CRightarrow%7C%28a%2Bi%20b%29%20z-z%7C%3D%7C%28a%2Bi%20b%29%20%5Cbar%7Bz%7D-0%7C%5C%5C%26%7Cz%28a%2Bi%20b-1%29%7C%3D%7C%28a%2Bi%20b%29%20%5Cbar%7Bz%7D%7C%5C%5C%26%5B%5Cbar%7Bz%7D%7C%7C%28a-1%29%2Bi%20b%7C%3D%7C%20z%7C%28a%2Bi%20b%29%7C%5C%5C%26%7Ca-1%2Bi%20b%7C%3D%7Ca%2Bi%20b%7C%5C%5C%26%5Csqrt%7B%28a-1%29%5E2%2Bb%5E2%7D%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%5C%5C%26%7Ca%2Bi%20b%7C%3D10%20%5Cquad%20a%5E2%2B1-2%20a%2Bb%5E2%3Dx%5E2%2Bb%5E2%5C%5C%26%5Csqrt%7Ba%5E2%2Bb%5E2%7D%3D10%5C%5C%26a%3D1%20%2F%202%5C%5C%26a%5E2%2Bb%5E2%3D100%5C%5C%26b%5E2%3D100-%5Cfrac%7B1%7D%7B4%7D%5C%5C)
![b^{2} =\frac{399}{4}](https://tex.z-dn.net/?f=b%5E%7B2%7D%20%3D%5Cfrac%7B399%7D%7B4%7D)
p = 399 and q= 4
p+q= 399+4
p+q=403
Hence the value of p+q = 403
Complete question:A function f is defined on the complex number by f (z) = (a + bi)z, where 'a' and 'b' are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that |a+bi|=8 and that
where p and q are coprime. Find the value of (p+q)
Learn more about complex numbers here:
brainly.com/question/20566728
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Answer:
its 2 homie
Step-by-step explanation:
1+1 equals 2 one thing plus another equals the next number.
Answer:
2² * 3⁴ * x * y³
Step-by-step explanation:
<h3>Simplify:</h3>
First prime factorize 324
324 = 2 * 2 * 3 * 3 * 3 * 3
Now , write in exponent form:
324 = 2²*3⁴
324xy³ =2² * 3⁴ * x * y³
Answer:
<h2>
The Slope Is <u>
12</u></h2>
Step-by-step explanation:
Below are the steps to follow to find the slope of any line.
First you need to pick two points. I chose (2,24) and (4,48). (It does not mater what points you chose.)
Now follow the equation
Slope (m) = ΔY/ΔX
ΔY = 48 – 24 = 24
ΔX = 4 – 2 = 2
24/2 = 12
Then no mater what points you chose, 12 should be your final answer
if Tim has read 10% of the book, that means he still hasn't read 90% of it yet, and we know that that 90% is 45 pages, so say the book has a total amount of pages of "x", which is 100%.
![\begin{array}{ccll} pages&\%\\ \cline{1-2} 45&90\\ x&100 \end{array}\implies \cfrac{45}{x}=\cfrac{90}{100}\implies \cfrac{45}{x}=\cfrac{9}{10} \\\\\\ 450=9x\implies \cfrac{450}{9}=x\implies 50=x](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccll%7D%20pages%26%5C%25%5C%5C%20%5Ccline%7B1-2%7D%2045%2690%5C%5C%20x%26100%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B45%7D%7Bx%7D%3D%5Ccfrac%7B90%7D%7B100%7D%5Cimplies%20%5Ccfrac%7B45%7D%7Bx%7D%3D%5Ccfrac%7B9%7D%7B10%7D%20%5C%5C%5C%5C%5C%5C%20450%3D9x%5Cimplies%20%5Ccfrac%7B450%7D%7B9%7D%3Dx%5Cimplies%2050%3Dx)