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3 years ago

Which way do you move when a question is asking which pair is located 5 units from point F? Point F being (3,-2)

Mathematics

1 answer:

valina [46]3 years ago

6 0

Answer:

Ann direction

Step-by-step explanation:

Given

$F = (3,-2)$

Required

Move 5 points from F

Generally, the direction to move the point is always stated. Since none is stated in this question, you can move the point in the positive or negative direction of the x and y coordinates (in other words, any direction).

So, the possible locations are:

$(3 + 5, -2) = (8, -2)$

$(3 - 5, -2) = (-3, -2)$

$(3, -2+ 5) = (3, 3)$

$(3, -2- 5) = (3, -7)$

Each of the above points are 5 units away from F

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Answer:

See proof below

Step-by-step explanation:

Let $r=\frac{w+z}{1+wz}$ . If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.

Remember this useful identity: if x is a complex number then $x\bar{x}=|x|^2$ where $\bar{x}$ is the conjugate of x.

Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):

$\frac{r}{\bar{r}}=\frac{w+z}{1+wz} \left(\frac{1+\bar{w}\bar{z}}{\bar{w}+\bar{z}}{\right)$

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Thus $\frac{r}{\bar{r}}=1$ . From this, $r=\bar{r}$ . A complex number is real if and only if it is equal to its conjugate, therefore r is real.

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