z=e^(2 times pi times i times t)
If t goes from 0 to 1, then you get the unit circle.
The complex number of the equation z = x + iy is x.
Yes, Microsoft Mathematics 4.0 can graph complex numbers and the unit circle. To graph complex numbers, you can enter them in the form (a + bi) (where (a) is the real part and (b) is the imaginary part) and plot them on the complex plane. To graph the unit circle, you can use the equation (x^2 + y^2 = 1), which represents all points with a distance of 1 from the origin. Simply input the equation in the graphing feature to visualize both the unit circle and any complex numbers on it.
the number that is part of the x-term
Standard equation for a circle centred at the origin is x2 + y2 = r2 where r is the radius of the circle. If you increase the size of the circle then the radius must increase, so r2 will be larger. eg a circle of radius 2 has the equation x2 + y2 = 4, if the radius increases to 3 then the equation becomes x2 + y2 = 9
The complex roots of an equation are the complex numbers that are solutions to the equation.
The complex number of the equation z = x + iy is x.
The radius of the circle decreases when you make the circle smaller.
the number that is part of the x-term
An algebraic number is a complex number which is the root of a polynomial equation with rational coefficients.
The x-coordinate of the circle's center changes when you move the circle horizontally. This is because the equation for a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle. Moving the circle horizontally shifts the circle left or right, changing the value of h.
The Radius
Standard equation for a circle centred at the origin is x2 + y2 = r2 where r is the radius of the circle. If you increase the size of the circle then the radius must increase, so r2 will be larger. eg a circle of radius 2 has the equation x2 + y2 = 4, if the radius increases to 3 then the equation becomes x2 + y2 = 9
(x2 + any number) + (y2 + any number) = 81
The complex roots of an equation are the complex numbers that are solutions to the equation.
The inner circle is x2 + y2 = 4. The radius of the inner circle is the square root of 4, which is 2. To find the radius of the outer circle, multiply 2 times 4. The radius of the outer circle is 8. Square 8 (82 or 8 x 8) to find the number to put into the equation of the outer circle. This is 64. The equation for the outer circle is x2 + y2 = 64.
The solution set is all points on the circle.
Because of how close the two are. The only difference between the two is that a complex number is any whole number along side of a fraction, while a real number is any positive number.