Mathematics, 03.10.2019 05:30, MoparorNocar061401

Which property of multiplication is shown below? if x = 3 + 4i and y = 5 + 6i, x × y = y × x.

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answered: genyjoannerubiera

Commutative property of multiplication

Step-by-step explanation:

According to commutative property of multiplication , for two elements x and y , we have $x\times y=y\times x$ .

Here, x = 3+4 i , y= 5+6 i

We will also use property : (a+b)(c+d)=a(c+d)+b(c+d)

$x\times y=\left ( 3+4i \right )\left ( 5+6i \right )\\=3\left ( 5+6i \right )+4i\left ( 5+6i \right )$

Also, we know that i^2 = -1

Therefore,

So,

$x\times y=\left ( 3+4i \right )\left ( 5+6i \right )\\=3\left ( 5+6i \right )+4i\left ( 5+6i \right )\\=15+18i+20i+24i^2\\=15+18i+20i-24\\$

On adding real and imaginary parts separately , we get

$x\times y=15+18i+20i-24\\=\left ( 15-24 \right )+i\left ( 18+20 \right )\\=-9+38i$

$y\times x=\left ( 5+6i \right )\left ( 3+4i \right )\\=5\left ( 3+4i \right )+6i\left ( 3+4i \right )\\=15+20i+18i+24i^2\\=\left ( 15-24 \right )+i\left ( 20+18 \right )\\=-9+38i$

So, $x\times y=y\times x$ .

Hence, commutative property is verified .

answered: Guest

step-by-step explanation:

19. what two-dimensional shape is formed by a cross section of the cube shown if the cross section p

answered: Guest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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Which property of multiplication is shown below? if x = 3 + 4i and y = 5 + 6i, x × y = y × x.

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