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3 years ago

(9 – 6i) × m = 9 – 6i What is m?

Mathematics

2 answers:

zhuklara [117]3 years ago

6 0

Answer:

The value of m would be 1

Step-by-step explanation:

Given equation,

$(9-6i)\times m=9-6i$

Divide both sides of the equation by 9 - 6i ( division property of equality )

We get,

$\frac{(9-6i)m}{9-6i}=\frac{9-6i}{9-6i}$

$\implies m=1$

Therefore, the value of m in the given equation would be 1.

Ann [662]3 years ago

4 0

M is equal to 1

good luck

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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.

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3 years ago

What is y=5x+3 when the x variable is 1

ikadub [295]

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Mumz [18]

Answer:

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Step-by-step explanation:

Given:

R = x²/y

x = 4.8 x 10⁵

y = 2.8 x 10⁴

Find:

Value of R

Computation:

R = x²/y

R = (4.8 x 10⁵)²/ (2.8 x 10⁴)

R = 23.04 x 10¹⁰ / (2.8 x 10⁴)

R = 8.22857.. x 10⁶

R = 8,228,571.43 (Approx)

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3 years ago

Find the perimeter of a triangle garden that measures 10 feet by x feet by (2 x+7) feet . Use p=a+b+c

tigry1 [53]

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= (10 + 7) + (x + 2x)

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3 years ago

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IrinaK [193]

Answer:

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Step-by-step explanation:

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