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Taking the square root of negative numbers leads to Complex Number (i). For example, the square root of -1 is equal to i . Complex numbers are in the form a + bi, where (a) is a real number and (bi) is the imaginary number.

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A example of complex numbers A complex number has the form x + yi where x and y are real numbers and i2 = −1.

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Modulus-take the square root of a^2 and b^2

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Jesus Trejo, Juan Limon, Matthew Requena 

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Jesus Trejo, Juan Limon, Matthew Requena 

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the geometric effect is when a point is changed by rotation,translation,reflection or dilation

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The angle measured from the positive real axis to the line segment; labeled θ

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Find argument by using tan inverse and divide by (b/a) If the  complex number is in the...

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1st=remains the same
2nd=-180
3rd=+180
4th=-360
https://mathsathome.com/modulus-argument-complex-number/

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To convert from degrees to radians, multiply the number of degrees by π/180.

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A complex number has two part it has the real number and the imaginary number an example would be z= a+ib a is the real part and ib is the imaginary part .

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Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

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the geometric interpretation of multiplication of complex numbers is stretching (or squeezing) and rotation of vectors in the plane.

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Multiplication of the complex numbers multiplies the two magnitudes, resulting in √130, and adds the two angles, 142∘.

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The length of the line segment is called the modulus of the complex number and is denoted |z| . The angle measured from the positive real axis to the line segment is called the argument of the complex number, denoted arg(z) a r g ( z ) and often labelled θ.

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To convert from polar to rectangular, find the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle.

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a different way to represent a complex number apart from rectangular form

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To change from radians to degrees, you need to multiply the number of radians by 180/π. This number will help you switch between the two units. For example, if you multiply π/2 radians by 180/π, you will get 90 degrees

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To change from radians to degrees, you need to multiply the number of radians by 180/π. This number will help you switch between the two units. (x)rad × 180/π = Degrees

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Innocent Mugisha , roxsana salazar,emanuel escobedo

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Innocent Mugisha , roxsana salazar,emanuel escobedo

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the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle

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To convert from polar form to rectangular form use given variables r and θ and use the transformation relations.
x = r ⋅ cos(θ)

y = r ⋅ sin(θ)
To convert from rectangular to polar form use:
r^2 = x^2 + y^2 ---> R
tan^-1 (y/x) ---> θ

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When multiplying complex numbers, its useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers.

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Multiplication of  complex numbers multiplies  two quantities, resulting in √130, and adds  two angles, 142∘. In other words, you can look at the second number by scaling and rotating the first (or by scaling the first  and rotating the second).

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Multiplication of  complex numbers multiplies  two quantities, resulting in √130, and adds  two angles, 142∘. In other words, you can look at the second number by scaling and rotating the first (or by scaling the first  and rotating the second).

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The different types of Geometric effects, are dilation, rotation, reflection or translation, it can also be rotated by 90-360 degrees, counter clockwise

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http://pirate.shu.edu/~wachsmut/complex/numbers/proofs/mult_geom.html

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To convert from degrees to radians, multiply the number of degrees by π/180. To find what it is in radians, you multiply 90 by π/180. This gives you π/2.

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Complex numbers are mathematical entities of the form (a + bi). The argument is the angle formed with the positive x-axis.

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The length of the line segment is called the modulus of the complex number and is denoted |z| . The angle measured from the positive real axis to the line segment is called the argument of the complex number, denoted arg(z) a r g ( z ) and often labelled θ .

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If you have an imaginary number in the denominator of a fraction you have to use something called 'the conjugate'.
In summary, the conjugate cancels the imaginary part of the denominator.
An example of when to use the conjugate is:

4+2i/3i

the first step is to find the conjugate:

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3i = -3i

the second step is to multiply the bottom & the top by the conjugate.

(-3i)(4+2i)/(3i)(-3i)

the last step is to multiply & solve

2-4i/3

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The argument of the complex number Z = a + ib is the angle θ which is the inverse of the tan function of the imaginary part divided by the real part of the complex number.

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To convert from degrees to radians, multiply the number by degrees of π/180.

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To convert from degrees to radians, multiply the number of degrees by pi/180.To find what it is in radians, you multiply 90 by pi/180.This gives you pi/2

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1 radian is the length of the radius wrapped around the circumference of the circle.
The radius of a circle can wrap around the circle 6 times but with a decimal value remaining ~0.28 so radians are multiplied by pi to make up for it, therefore 2*(~3.14)=(~6.28)=360 degrees

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this is the thumbnail of a video with good learning source

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A video that explains how this techniche works