Complex number (English)
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Definition (keystage 3)
Complex numbers consist of a real number plus an imaginary number. If we think of imaginary numbers as having a number line of their own at right angles to the ordinary real number line, then complex numbers exist in a plane called the complex plane. The real and imaginary part are like x and y co-ordinates.
Definition (advanced level)
A real number, plus a real multiple of i, where i2=−1.
We use the symbol C for the set { x+iy|x,y ∈ R } .
We use the symbol C for the set { x+iy|x,y ∈ R } .
Relations
- broader:
- (en) Number
- narrower:
- (en) Complex conjugate
- (en) Euler's formula for complex numbers
- (en) Gaussian integer
- (en) Imaginary number
- (en) Real number
- references:
- (en) Reciprocal of a complex number
- referenced:
- (en) Analytic function
- (en) Argand
- (en) Complex addition formula
- (en) Fundamental theorem of algebra
- (en) Modulus of a number
- (en) Modulus-argument form
- (en) Riemann hypothesis
- (en) Sesquilinear form
- (en) The exponential function is periodic
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