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Mathematics

1 answer:

leonid [27]4 years ago

5 0

The second choice, y+1=6/11(x+4), is correct.

We first find the slope using the formula

m=(y₂-y₁)/(x₂-x₁)

Using our points, this gives us
m=(-1-5)/(-4-7) = -6/-11 = 6/11

Point-slope form is
y-y₁=m(x-x₁)

Using the first point, we would have
y-5=6/11(x-7)

Using the second point, we would have
y--1=6/11(x--4)
y+1=6/11(x+4)

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marysya [2.9K]

The product is equal to:

$\frac{18}{25}(cos(165) + i*sin(165))$

<h3>How to solve the product?</h3>

Remember that we can write a complex number in polar form as:

$R*e^{i*a} = R*(cos(a) + i*sin(a))$

Then the given product:

$\frac{6}{5}*(cos(120) + i*sin(120))*\frac{3}{5}*(cos(45) + i*sin(45))$

can be rewritten to:

$(\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})$

Now is easier to solve the product:

$(\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})\\\\= \frac{6}{5} *\frac{3}{5} *e^{i*(120 + 45)}\\\\= \frac{18}{25}*e^{i*165}\\\\= \frac{18}{25}(cos(165) + i*sin(165))$