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Q: Mapping of complex numbers in complex plane?

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It helps to visualize the numbers on a plane. The complex numbers occupy the entire plane. The real numbers are all the numbers on the horizontal axis, the imaginary numbers are all the numbers on the vertical axis. A complex number thus has a real and an imaginary part, a + bi, where a and be are real numbers (for example, 3 - 2i).

The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.

In the Argand diagram (complex plane), numbers on the horizontal axis represent real numbers.

The horizontal axis is the real numbers.

The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".

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All complex numbers are part of the "complex plane", so none of them is farther than others.

It helps to visualize the numbers on a plane. The complex numbers occupy the entire plane. The real numbers are all the numbers on the horizontal axis, the imaginary numbers are all the numbers on the vertical axis. A complex number thus has a real and an imaginary part, a + bi, where a and be are real numbers (for example, 3 - 2i).

Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.

The answer depends on the domain. If the domain is non-negative real numbers, then the range is the whole of the real numbers. If the domain is the whole of the real numbers (or the complex plane) , the range is the complex plane.

The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.

In the Argand diagram (complex plane), numbers on the horizontal axis represent real numbers.

It could be the Real numbers or it could be the Complex plane.

The horizontal axis is the real numbers.

The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".

It could be the system of straight line equations that are plotted on the Cartesian plane.

whet is real and complex plane

The whole of the Real numbers, or even the whole of the complex plane.

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