Imaginary number (English)
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Definition Niveau 2
The square roots of 9 are 3 and -3.
The square roots of 4 are 2 and -2.
The square roots of 1 are 1 and -1.
We notice that -1 and other negative numbers don't have square roots. But sometimes it would be very useful if every number had a square root.
So we imagine that there is a number, called i, which is defined by saying that when you square it you get -1.
So then the square roots of -1 are i and -i.
The square roots of -4 are 2i and -2i.
etc.
We call i, 2i, etc. imaginary numbers, and we say that they lie along a number line like the ordinary, real, number line, but at right angles to it. These two number lines together form a plane called the complex plane.
The square roots of 4 are 2 and -2.
The square roots of 1 are 1 and -1.
We notice that -1 and other negative numbers don't have square roots. But sometimes it would be very useful if every number had a square root.
So we imagine that there is a number, called i, which is defined by saying that when you square it you get -1.
So then the square roots of -1 are i and -i.
The square roots of -4 are 2i and -2i.
etc.
We call i, 2i, etc. imaginary numbers, and we say that they lie along a number line like the ordinary, real, number line, but at right angles to it. These two number lines together form a plane called the complex plane.
Beziehungen:
- weiterer Begriff:
- (en) Complex number
- engerer Begriff:
- (en) i
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