Find the value of the underlined 10,698 under lined digit is 9

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

A triangle is removed from the rectangle. Find the area of the remaining figure.

Mariulka [41]

Answer

C) 160 in^2

Step by step explanation

First, let's find the area of the rectangle.

Area of a rectangle = length x width

The area of the rectangle = 20 * 10

= 200 in^2

Now let's find the area of the triangle that is removed.

Area of a triangle = 1/2 base * height.

Here base = 10 and height = 8. Plug in these values into the formula, we get

Area of the triangle = 1/2 * 10*8

= 5* 8

The area of the triangle = 40 in^2

The area of the remaining figure = Area of the rectangle - area of the triangle

= 200 - 40

= 160 in^2

The answer is "160 in^2"

Thank you.

5 0

3 years ago

Elena has a bottle that has a capacity of 34 quarts. What is the maximum amount of liquid that can be stored in this bottle?

katovenus [111]

I would say 8.5 gallons

4 0

3 years ago

What are the coordinates of the center and length of the radius of the circle whose equation is X^2+6x+4y=23?

Virty [35]

Answer:

The following equation is not a circle, but a hyperbola, because you have 4y, but no y^2

Step-by-step explanation:

Please mark for Brainliest!! :D Thanks!!

For more questions or more information, please comment below!

3 0

3 years ago

Write a decimal equation that has a product of 3.15

Vaselesa [24]

<span>you could have 3.15=100 times 0.0315, 10 times 0.315.</span>

4 0

3 years ago