How can a conjugate be created from a complex number?

2 answers:

8 0

A conjugate can be created from a complex number The complex conjugate formula is a+bi is a -bi change the signs of the complex number (a-bi is a+bi) the real part is left unchanged.

ratelena [41]3 years ago

5 0

Remember that (a-b)(a+b)=a²-b²
and (imaginary number)²=real

so if we have a+bi, then a-bi is the conguate because (a+bi)(a-bi)=a²+b²

if the complex number is a+bi the conjucate is a-bi

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Multiply 9(6/7) and write the result I. simplest form? please show me the step

GarryVolchara [31]

ANSWER:

The answer would be C. 54/7

EXPLANATION:

Multiply 9* 6/7 = 9x6/1x7 = 54/7

Multiply both nominators and denominators
Result to keeping the lowest possible denominator GCD(54, 7).

GCD - 54 / 1 = 53
7 / 1 = 7

8 0

2 years ago

The question is, "Find the volume of the bodies given in the figures below, which have a hole along their entire length." How do

aniked [119]

Answer:

1782 cm³

Step-by-step explanation:

First, you measure the volume of the cuboid as a whole which is length x breadth x height, 9 x 12 x 18 = 1944 cm³. Then measure the volume occupied by the space, 3 x 3 x 18 since the hole runs along the entire length = 162 cm³.

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4 0

2 years ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

A rectangular prism is 4 inches long, 3 inches wide and 8 inches tall . Eli packs the prism with unit cubes to find the volume.

bulgar [2K]

Answer:

$V=96\ inch^2$