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1/12/14

Complex Number Trigonometric Form.

complex number form:

(a,b) = a + i * b.


is most commonly used. often though it's convenient to use trigonometric form, which is consequence of interpreting complex number (a,b) as a point on plane (so called 'complex plane') with coordinates a and b.

precisely, taking:

|z| = sqrt(a2+b2) ; where sqrt is square root function.


and angle φ such as:

sin φ = b/|z|, cos φ = a/|z|,


we get:

z = |z|(cos φ + i sin φ).


this is trigonometric form. real number |z| we call modulus of complex number z, and φ it's argument, φ = arg z.

if z ≠ 0 and we assume that φ belongs to [0, 2*Pi) then trigonometric form is unambiguously set. we can write then: φ = Arg z.


Source: [1].


See also: Complex Numbers Body.

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