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IgorLugansk [536]
3 years ago
14

The point A,B,C and D represent the complex number Z1,Z2,Z3 and Z4 and O is the origin. If OABC is a parallelogram, and Z1=1+3i

and Z2=4+5i, find Z3
Mathematics
1 answer:
aleksley [76]3 years ago
8 0

Complex numbers are divided into two parts; real and imaginary parts. The value of Z3 is 5+ 8i

Given that:

Z_1 = 1 + 3i

Z_2 = 4 + 5i

Since O is the origin, then:

C = OA + OB

This means that:

Z_3 = Z_1 + Z_2

So, we have:

Z_3 = 1 + 3i + 4 + 5i

Collect like terms

Z_3 = 1 + 4+ 3i  + 5i

Z_3 = 5+ 8i

Hence, complex number Z3 is 5+ 8i

Read more about complex numbers at:

brainly.com/question/18509723

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podryga [215]

Answer: Choice B

(-2, 5)

==================================================

Explanation:

The original system is

\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}

Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations

\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}

Now add straight down

The x terms add to -4x+3x = -1x = -x

The y terms add to 3y+(-3y) = 0y = 0

The terms on the right hand sides add to 23+(-21) = 2

We end up with the equation  -x = 2 which solves to x = -2

Now use this to find y. You can pick any equation with x,y in it

----------------

-4x+3y = 23

-4(-2)+3y = 23

8+3y = 23

3y = 23-8

3y = 15

y = 15/3

y = 5

Or

x-y = -7

-2-y = -7

-y = -7+2

y = -5

y = 5

Either way, we get the same y value.

So that's why the solution is (x,y) = (-2, 5)

6 0
3 years ago
What system shows the correct numbers to multiply by the coefficients in order to eliminate y from the first two
Ann [662]

Answer:

3 (5x+2y = 0)

2 (2x – 3y = -19)

Step-by-step explanation:

5x+2y=0 (1)

2x-3y=-19 (2)

To eliminate y from the first two equation when applying the linear combination method

We will multiply y Equation (1) and (2) with 3 and 2 respectively so that the coefficients of y in the two equations +6 and -6 respectively

3(5x+2y=0)

2(2x-3y=-19)

We have,

15x+6y=0 (3)

4x-6y= -38 (4)

Add Equation (3) and (4)

19x=-38

x= -2

Substitute x= -2 into (1)

5x+2y=0

5(-2)+2y=0

-10+2y=0

-10= -2y

y=-10/-2

=5

y=5, x=-2

3 0
3 years ago
What is the equivalent percent fraction for 1/2 3/4 7/10 3/20 4/25 9/50 1/8
ohaa [14]

Answer:1/2=0.5

3/4=0.75

7/10=0.7

3/20=0.15

4/25=0.16

9/50=0.18

1/8=0.125

Step-by-step explanation:

1/2=0.5

3/4=0.75

7/10=0.7

3/20=0.15

4/25=0.16

9/50=0.18

1/8=0.125

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Compare and contrast expanding and simplifying algebraic expressions with simplifying numeric expressions. For example, compare
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<span>With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.</span>
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3 years ago
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Which fraction is equal to 0.98
Harrizon [31]

The most simplified version of it is 49/50

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3 years ago
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