NEED HELP FAST PLEASE.

Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

3 0

3 years ago

Solve by substitution

Hunter-Best [27]

Answer:

A

Step-by-step explanation:

y = -9 ------(1)

9x -4y = -9 -------(2)

substitute (1) into (2)

9x - 4 (-9) = -9

9x = - 45

x = -5

there you go, x = -5 and y = -9

so. (-5 , -9 )

hope this helps

please mark it brainliest

7 0

2 years ago

Describe how to convert from vertex form to standard form. (10 points

Anton [14]

Answer:

"simplify" it

Step-by-step explanation:

To convert from vertex form to standard form for a quadratic, eliminate parentheses and collect terms. In short, "simplify" it.

7 0

2 years ago

Explain why the expression 9x^3+1/2x^2+3x^-1 is not a polynomial

Nastasia [14]

Answer:

The given expression can't be expressed in polynomial form. Hence, it is not a polynomial.

Step-by-step explanation:

P(x,n) is a polynomial of nth degree if it is of the form,

P(x,n) = $a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3} + ......... +a_{n}x^{n}$

where n is a finite positive integer and n ∈ N

and ' $a_{i}$ 's are fixed but otherwise arbitrary constants ∀ i = 0(1)n .

Now, the given expression is,

$9x^{3} + \frac {1}{2x^{2}} + 3x^{-1}$

which doesn't fit in the above form. Hence, it is not a polynomial.

4 0

3 years ago

Honestly, I'm trying my best to solve this but my Math XL is being so rude.

Valentin [98]

<h3>Answer: 19</h3>

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Explanation:

T is the midpoint of PQ, which means T splits PQ into two equal parts. Those parts being PT and TQ.

Set them equal to each other and solve for x.

PT = TQ

3x+7 = 7x-9

3x-7x = -9-7

-4x = -16

x = -16/(-4)

x = 4

So,

PT = 3x+7 = 3*4+7 = 19

TQ = 7x-9 = 7*4-9 = 19

Both PT and TQ are 19 units long to help confirm the answer.

5 0

2 years ago

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