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Anton [14]
3 years ago
10

Algebra 2

Mathematics
1 answer:
denis23 [38]3 years ago
3 0

Answer:

Complex numbers are the one having two parts:

  • Real part
  • Imaginary part

Each of the part is simplified to (a+ib) format.

I hope it will help you.

Step-by-step explanation:

All parts are solved below:

Part 1:

=(-8i) + (41)+(-3 - 7i)

opening brackets

=-8i+41-3-7i

Adding like terms, real to real and imaginary to imaginary

= 38-15i

Part 2:

= (7 + 5i) - (7 - i)

Negative sign before bracket will change the signs to opposite

=7+5i - 7+ i

Adding like terms, real to real and imaginary to imaginary

=0 + 6i

Part 3:

=(8 – 4i) - (5 – 4i)

Negative sign before bracket will change the signs to opposite

= 8-4i-5+4i

Adding like terms, real to real and imaginary to imaginary

=3+0i

Part 4:

=(-8 - 4i) - (8 + i)

Negative signs before bracket will change the signs to opposite

=-8-4i-8-i

Adding like terms, real to real and imaginary to imaginary

=-16-5i

Part 5:

=(-3 - i) + (7 + 2i)

=-3-i+7+2i

Adding like terms, real to real and imaginary to imaginary

=4+1i

Part 6:

=-2 +6-(-4 + 2i)

Negative sign before bracket will change the signs to opposite

=-2+6+4-2i

Adding like terms, real to real and imaginary to imaginary

=8-2i

Part 7:

=(3 - 8i)(-4 + 4i)

Multiplying both bracket we get:

=-12+12i+32i+32i^2

By putting   i^2 = (-1)  

=12 +44i + 32 (-1)

Adding like terms, real to real and imaginary to imaginary

= -20+44i

Part 8:

=(5 – 3i)(-7 - 2i)

Multiplying both bracket we get:

=-35-10i+21i+6i^2

=-31+11i + 6 (-1)   (By putting   i^2 = (-1))

Adding like terms, real to real and imaginary to imaginary

=-37+11i

Part 9:

=8 + 8i

Part 10:

=(7 - 5i)(-4 + 3i)

Multiplying both bracket we get:

=-28+21i+20i-15i^2        (By putting   i^2 = (-1))

=-28+41i- 15(-1)

Adding like terms, real to real and imaginary to imaginary

=-13+41i

Part 11:

=7 + 4i

Part 12:

=(8 - 7i)(3 - 3i)

Multiplying both bracket we get:

=24-24i-21i+21i^2

=24-45i+21(-1)            (By putting   i^2 = (-1))

Adding like terms, real to real and imaginary to imaginary

=3-45i

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Solve the system by graphing.
igor_vitrenko [27]

Answer:

Hi There the correct answer is {x,y} = {-1,-10}  

 

System of Linear Equations entered :

  [1]    3x - y = 7

  [2]    4x - 2y = 16

Graphic Representation of the Equations :

   y + 3x = 7        -2y + 4x = 16  

 

 

Solve by Substitution :

// Solve equation [1] for the variable  y  

 

 [1]    y = 3x - 7

// Plug this in for variable  y  in equation [2]

  [2]    4x - 2•(3x-7) = 16

  [2]    -2x = 2

// Solve equation [2] for the variable  x  

  [2]    2x = - 2  

  [2]    x = - 1  

// By now we know this much :

   x = -1

   y = 3x-7

// Use the  x  value to solve for  y  

   y = 3(-1)-7 = -10  

Solution :

{x,y} = {-1,-10}  

Hope it helps!

8 0
3 years ago
Solve.
bixtya [17]

Answer:

-3 ± 2\sqrt{3} = x

Step-by-step explanation:

x² + 6x + 9 = 12 → x² + 6x - 3

Since this Quadratic Expression is unfactorable, apply the <em>Quadratic</em><em> </em><em>Formula</em>:

x = -b ± \frac{\sqrt{{b}^{2} - 4ac}}{2a}

-6 ± \frac{\sqrt{{6}^{2} - 4(1)(-3)}}{2(1)} =   -6 ± \frac{\sqrt{36 + 12}}{2} = -6 ± \frac{\sqrt{48}}{2} \\ \\ -3 ± 2\sqrt{3}

√48 = √[3 × 16] = 4√3

½[4√3] = 2√3

Then attach half of -6 to it as well [-3]:

-3 ± 2√3

I am joyous to assist you anytime.

7 0
3 years ago
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