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3 years ago

3+5i/-2+3i perform operation

Mathematics

1 answer:

melisa1 [442]3 years ago

4 0

Answer:

$\dfrac{9}{13}-\dfrac{19}{13}i$

Step-by-step explanation:

Remember $i^2=-1$

You are given the fraction $\dfrac{3+5i}{-2+3i}$

First, multiply the numerator and the denominator by -2-3i:

$\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}$

This gives you 13 in denominator, now multiply two complex numbers in numerator:

$(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i$

Thus, the initial fraction is

$\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i$

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3 years ago

Which expressions are equivalent to Negative 9 (two-thirds x + 1)? Check all that apply.

Sav [38]

Answer:

$-9(\frac{2}{3}x) + 9(1)\\ \\-6x + 9$

Explanation:

Before we begin, remember the following rules:

1- Distribution property:

$a(b+c) = ab+ac$

2- Simplification of fractions:

$\frac{xy}{yz}=\frac{x}{z}$

3- Signs in multiplication:

+ve * +ve = +ve

-ve * -ve = +ve

+ve * -ve = -ve

Now, for the given problem, we have:

$9 (\frac{2}{3}x + 1)$

Starting with the distributive property:

$-9 (\frac{2}{3}x +1) = -9(\frac{2}{3}x) - (-9)(1) = -9(\frac{2}{3}x) + 9(1)$

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Now, we simplify the output from the above step:

$-9(\frac{2}{3}x) + 9 = \frac{-9*2}{3}x + 9 = -6x+9$

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Hope this helps :)

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I need help i will give brainiest question in screenshot

Thepotemich [5.8K]

Answer:

ok so first you have to know what a reflectiin along 180 is

) A point P(x,y)P(x,y) is rotated 180180 degrees about the origin, then reflected over the y-axis. What is the resulting image of PP?

My conjecture: (−x,y)(−x,y) but I don't quite agree with it graphically. I'm having trouble with what exactly a 180 degree rotation about the origin simply is.

2) A point P(x,y)P(x,y) is reflected over the y-axis and then rotated 180 degrees about the origin. What is the resulting image?

Is this the same thing as 1?

3) A point A(x,y)A(x,y) is reflected over the line y=xy=x and then reflected over the y-axis. What is the resulting image of A?

My conjecture: (−y,x)(−y,x)

4) A point A(x,y)A(x,y) is reflected over the lines y=−xy=−x and then reflected over the y-axis. What is the resulting image of A?

My conjecture: (y,−x)

ok you need to know what thouse meen

Step-by-step explanation:

)If P(x1,y1)P(x1,y1) is rotated angle ϕϕ about O(a,b)O(a,b) to P′(x′,y′)P′(x′,y′)

we have |OP|=|OP′||OP|=|OP′| and |arctanmOP−arctanmOP'|=ϕ|arctan⁡mOP−arctan⁡mOP'|=ϕ

By atan(z)(z) I imply atan2

(2)If P(x1,y1)P(x1,y1) is reflected over L:ax+by+c=0L:ax+by+c=0 and the resulting image of PP is Q(x2,y2) (1)Q(x2,y2) (1)

We have R

so i hope thiz helprs you

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