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Q: What is the complex number of z 2 - Ii?

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The possible values of z are (a cis b), where a is any number between and including 0 and 2 and b is any of 0, 60, 120, 180, 240 and 300 degrees. The minimum modulus of z - 2, that is |z - 2|, is 0.

Yes and it is z=x+iy

You can use another complex number, a real number or an imaginary number. Complex number equations make interesting images. The link shows the image produced by (z-1)/(z+1) and inverses the checkerboard around two points.

A complex number is denoted by Z=X+iY, where X is the real part and iY is the imanginary part. So the number 4 would be 4+i0 and is the real part of a complex number and so 4 by itself is just a real number, not complex.

1. A complex formula like (z+1/z) is used to study and design airplane wings. 2. I use complex numbers to make math related art. The LINK below shows artwork based on the formula (z-1)/(z+i)

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Given a complex number z = a + bi, the conjugate z* = a - bi, so z + z*= a + bi + a - bi = 2*a. Note that a and b are both real numbers, and i is the imaginary unit: +sqrt(-1).

There are no real reason why it is denoted by z, but that the real number axis is denoted by x, imaginary number is denoted by y, the real part of a complex number is denoted by a, the imaginary part of a complex number is denoted by b, so there is z left.

In complex mode functions, modules, and procedures cannot operate. For a complex number z = x + yi, first define the absolute value. This would be |z| and is the distance from z to 0 in the complex plane.

The possible values of z are (a cis b), where a is any number between and including 0 and 2 and b is any of 0, 60, 120, 180, 240 and 300 degrees. The minimum modulus of z - 2, that is |z - 2|, is 0.

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Yes and it is z=x+iy

You can use another complex number, a real number or an imaginary number. Complex number equations make interesting images. The link shows the image produced by (z-1)/(z+1) and inverses the checkerboard around two points.

A COMPLEX NUMBER CAN BE CONVERTED INTO A POLAR FORM LET US TAKE COMPLEX NUMBER BE Z=a+ib a is the real number and b is the imaginary number THEN MOD OF Z IS SQUARE ROOT OF a2+b2 MOD OF Z CAN ALSO BE REPRESENTED BY r . THEN THE MOD AMPLITUDE FORM IS r(cos@Very interesting, but -i is not a complex no. it is a simple (imaginary) no. with no real part.

Yes. This can be verified by using a "generic" complex number, and multiplying it by its conjugate: (a + bi)(a - bi) = a2 -abi + abi + b2i2 = a2 - b2 Alternative proof: I'm going to use the * notation for complex conjugate. Any complex number w is real if and only if w=w*. Let z be a complex number. Let w = zz*. We want to prove that w*=w. This is what we get: w* = (zz*)* = z*z** (for any u and v, (uv)* = u* v*) = z*z = w

A complex number (z = x + iy) can be plotted the x-y plane if we consider the complex number the point (x,y) (where x is the real part, and y is the imaginary part). So once you plot the complex number on the x-y plane, draw a line from the point to the origin. The Principle Argument of z (denoted by Arg z) is the measure of the angle from the x-axis to the line (made from connecting the point to (0,0)) in the interval (-pi, pi]. The difference between the arg z and Arg z is that arg z is an countably infinite set. And the Arg z is an element of arg z. Why? : The principle argument is needed to change a complex number in to polar representation. Polar representation makes multiplication of complex numbers very easy. z^2 is pretty simple: just multiply out (x+iy)(x+iy). But what about z^100? This is were polar represenation helps us, and to get into this representation we need the principle argument. I hope that helped.

Magnitude

z=rl +XL in a series circuit. if XL increases and r remains the same, z will increase. z is a complex number and the magnitude is z=(r^2 + (XL)^2)^.5. if the vector part of z increases z increases.

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