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4 years ago

Which of the following expressions is the conjugate of a complex number with −6 as the real part and −5i as the imaginary part?

2 answers:

5 0

The complex number is -6-5i. The conjugate means just flip the sign of the imaginary part of the complex number. -6+5i is the answer.

MrMuchimi4 years ago

3 0

Answer:

Conjugate of complex number is -6 + 5i

Step-by-step explanation:

a complex number with −6 as the real part and −5i as the imaginary part

For a complex number a+ib

a is the real part and b is the imaginary part

a complex number with −6 as the real part and −5i as the imaginary part can be written as -6-5i

the conjugate of a+ib is a-ib

The conjugate pf -6 -5i is -6+5i

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4 years ago

Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so

alex41 [277]

Answer:

The equation is $x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0$

Step-by-step explanation:

From the question we are told that

The diameter endpoints is (-8, -3, -10) and (-6, 1, -4)

Generally the equation of a sphere with center coordinates (a, b , c ) and radius r is mathematically represented as

$(x - a )^2 + (y -b )^2 + (z -c)^2 = r^2$

Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows

$(a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ]$

$(a, b , c) = [ -7 , -1.5 , -7 ]$

Now the length of the diameter is evaluated as

$|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }$

$|d| = \sqrt{56 }$

$|d| = \sqrt{4 * 14 }$

$|d| = 2 \sqrt{ 14 }$

Now the radius is mathematically represented as

$r = \frac{|d|}{2}$

$r = \frac{ 2 \sqrt{14} }{2}$

$r = \sqrt{14}$

$(x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2$

$(x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14$

$x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14$

$x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0$

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4 years ago

PLEASE HELP! WILL GIVE BRAINLIEST!

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Answer:

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Step-by-step explanation:

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3 years ago

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4 years ago

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3 years ago