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Ray Of Light [21]
2 years ago
7

The sum of two complex numbers is −3 + 5i. If one of the complex numbers is 1−8i, which answer choice below is the other number?

Mathematics
1 answer:
AnnyKZ [126]2 years ago
6 0

Answer:

C

Solution

For a complex number written in the form a + bi, a is called the real part of the complex number and b is called the imaginary part. The sum of two complex numbers, a + bi and c + di, is found by adding real parts and imaginary parts, respectively, that is, (a + bi) + (c + di) = (a + c) + (b + d)i. Therefore, the sum of 2 + 3i and 4 + 8i is (2 + 4) + (3 + 8)i = 6 + 11i.

Choice A is incorrect and is the result of disregarding i and adding all parts of the two complex numbers together, 2 + 3 + 4 + 8 = 17. Choice B is incorrect and is the result of adding all parts of the two complex numbers together and multiplying the sum by i. Choice D is incorrect and is the result of multiplying the real parts and imaginary parts of the two complex numbers, (2)(4) = 8 and (3)(8) = 24, instead of adding those parts together.

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Answer:

(x - 2)² + (y + 3)² = 32

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre of the circle is at the midpoint of the diameter

Calculate the centre (x, y ) using the midpoint formula

(x, y ) = ( \frac{x_{1}+x_{2}  }{2} , \frac{y_{1}+y_{2}  }{2} )

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (6, - 7)

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The radius is the distance from the centre to either of the endpoints

Calculate the radius using the distance formula

r = \sqrt{(x_{2}-x_{1})^2+( y_{2}-y_{1})^2   }

with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (- 2, 1)

r = \sqrt{(-2-2)^2+(1-(-3))^2}

  = \sqrt{(-4)^2+(1+3)^2

   = \sqrt{16+4^2}

   = \sqrt{16+16}

   = \sqrt{32}

Then equation of circle is

(x - 2)² + (y - (- 3) )² = (\sqrt{32} )² , that is

(x - 2)² + (y + 3)² = 32

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