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
In the standard equation for a circle centered at the origin, ( x^2 + y^2 = r^2 ), the radius ( r ) determines the size of the circle. When you make the circle smaller, you decrease the radius ( r ). Consequently, the value of ( r^2 ) also decreases, resulting in a smaller circle. Thus, the number that decreases in the equation is ( r^2 ).
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 number of the equation z = x + iy is x.
The radius of the circle decreases when you make the circle smaller.
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
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 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 complex roots of an equation are the complex numbers that are solutions to the equation.
The solution set is all points on the circle.