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Fungrim entry: 77d6bf

ea+bi=ea(cos(b)+sin(b)i){e}^{a + b i} = {e}^{a} \left(\cos(b) + \sin(b) i\right)
Assumptions:aC  and  bCa \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
TeX:
{e}^{a + b i} = {e}^{a} \left(\cos(b) + \sin(b) i\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
Coscos(z)\cos(z) Cosine
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("77d6bf"),
    Formula(Equal(Exp(Add(a, Mul(b, ConstI))), Mul(Exp(a), Add(Cos(b), Mul(Sin(b), ConstI))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC