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Complex Numbers

The square root of negative one, which we now call the imaginary unit, was once thought to be an absurd notion. However, through the diligent studies of open-minded mathematicians, it was shown that the real numbers were actually just one part of a larger set of numbers known as the complex numbers, the other part being the imaginary numbers. Please direct all questions about these surprisingly useful and applicable numbers into this category.

500 Questions

How many times does 18 go into 99?

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0.18181818181818182

Is -7 a complex number?

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Yes, all real numbers are complex numbers.

How are complex numbers and real numbers related?

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Complex numbers extend the concept of real numbers by introducing an imaginary unit, denoted as "i." Real numbers can be considered a subset of complex numbers with the imaginary part equal to zero. Complex numbers include both a real and imaginary component, allowing for operations like addition, subtraction, multiplication, and division.

What is the first step when dividing complex numbers?

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The first step when dividing complex numbers is to find the conjugate of the denominator, which is the same expression but with the sign of the imaginary part changed. This is done to eliminate the imaginary part in the denominator.

Mapping of complex numbers in complex plane?

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In the complex plane, each complex number is represented by a point, with the real part as the x-coordinate and the imaginary part as the y-coordinate. The mapping of complex numbers in the complex plane allows us to visualize operations like addition, subtraction, multiplication, and division geometrically. It also enables us to study properties such as modulus, argument, and conjugate of complex numbers.

Where are negative numbers used in every day life?

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The temperature of a fridge or a bank overdraft

How zeros are in a bicentillion?

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A: "bicentillion" doesn't exist, I think you mean: centillion, or here in Britan a vigintillion, a vigintillion has 120 zeros after it and a centillion has 303 zeros after it.

Where is Gangnam-gu?

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Gang-nam is a city in south Korea where Psy was raised it translates into English as city south of river it is a business city but Psy claims the style there is dress classy act cheesy

so when Psy says Gang-nam style he means in the style of the people of Gang-nam

What are the applications of complex numbers in civil engineering and building?

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This is a rather loose application. The related link shows the fluid flow field of two

water sources near each other.

Refer to related link down below.

How to calculate sum of two complex number in c plus plus?

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typedef struct complex {

double real, imag;

} complex;

...

complex x, y, z;

...

/* add */

z.real = x.real + y.real;

z.imag = x.imag + y.imag;

/* sub */

z.real = x.real - y.real;

z.imag = x.imag - y.imag;

/* mul */

z.real = x.real*y.real - x.imag*y.imag;

z.imag =x.imag*y.real + x.real*y.imag;

/* div */

double d = y.real*y.real + y.imag*y.imag;

z.real = (x.real*y.real + x.imag*y.imag)/d;

z.imag = (x.imag*y.real - x.real*y.imag)/d;

Which set of number does not contain 70?

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There is an infinite number of answers, but anything that is divisible by 3, 6, 8, 9, 11, 12, 13 and so on

eg 3, 6, 9, 12...

eg 11, 22, 33, 44...

eg 13, 26, 39, 52,

What is conjugation of 7-2i?

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The conjugate of a complex number can be found by multiplying the imaginary part by -1, then adding the "real" part back. (-2i) * -1 = 2i, so the conjugation is 7+2i

How do you solve complex fraction?

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this is a very good question. lets solve (2+3i)/(4-2i).

we want to make 4-2i real by multiplying it by the conjugate, or 4+2i

(4-2i)(4+2i)=16-8i+8i+4=20, now we have

(2+3i)/20 0r 1/10 + 3i/20

notice that -2i times 2i = -4i^2 =-4 times -1 = 4

What are some unique properties of imaginary numbers?

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1. i1 = i, i2= -1, i3= -i, i4= 1, i5= i, i6= -1 and so on.

2. Euler's constant e, when raised to the power of a complex number, gives a point in the complex plane according to Euler's Identity, e^(iθ

) = cos(θ

) + i*sin(θ

).

Whenθ

is replacedby pi, we get:

e^(iπ)

= cos(π

) + i*sin(π

)

= -1 + 0

= -1

In other words, e^(iπ)

+ 1 = 0.


3. Many intriguing fractals have been discovered in the complex plane, the most famous of which is the Mandelbrot Set. This is formed by an iterative process of a point in the plane. It produces a beautiful image, nicknamed by many as the "Thumbprint of God". (Google Images is your friend here - check it out.)


4. De Moivre's Theorem holds true in the realm of the imaginary, stating that

(r cisθ

)n= rncis nθ

.

This is a fascinating theorm in itself, but it also has hidden implications.

For example, if r = 1 (the point was 1 unit away from the origin), and you were to plot this point with a small angle above the positive real axis, then raising this number to an increasing power would result in that point making a full revolution about the origin and coming right back to where it started.

This is because rnstays the same (1^(anything) = 1), but the angle is slowly increasing as the power does. Therefore, as the angle increases, a circle is plotted around the origin with radius 1.


There are many other fascinations around complex numbers, but this covers the basics.

How write in words the number 5280?

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five thousand two hundred eighty

What is the GCF of 15 and 36 with work?

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3 x 5 = 15

2 x 2 x 3 x 3 = 36

The GCF is 3.

Example of similar fraction?

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Similar factions are fraction that have the same denominator ^^

How much is 67 pounds in kilograms?

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i weigh 67 kg and wont to know how much that is in pounds