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3 years ago

11

A complex number is shown with a real part of 7 and an imaginary part of -3i. Choose the complex conjugate of the complex number

.

1 answer:

UNO [17]3 years ago

6 0

7+3i is the correct answer as conjugate is only changing the sign

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3 years ago

Write the equation of the line that passes through the points (-6,5) and (3,−5). Put your answer in fully reduced point-slope fo

elena55 [62]

Answer:

$\displaystyle y-5=-\frac{10}{9}(x+6)$

Or:

$\displaystyle y+5=-\frac{10}{9}(x-3)$

Step-by-step explanation:

We want to write the equation of a line that passes through the points (-6, 5) and (3, -5) in point-slope form.

Point-slope form is given by:

$y-y_1=m(x-x_1)$

Thus, first, we need to find the slope. We can use the slope formula:

$\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{(-5)-(5)}{(3)-(-6)}=\frac{-10}{9}=-\frac{10}{9}$

Next, we can use either of the two given points. I'll use (-6, 5). So, let (-6, 5) be (<em>x₁, y₁</em>). Substitute:

$\displaystyle y-(5)=-\frac{10}{9}(x-(-6))$

Or, fully simplified:

$\displaystyle y-5=\frac{-10}{9}(x+6)$

Using the other point, we will acquire:

$\displaystyle y-(-5)=-\frac{10}{9}(x-(3))$

Or, simplified:

$\displaystyle y+5=-\frac{10}{9}(x-3)$

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3 years ago