{"id":31923,"date":"2020-09-30T21:22:00","date_gmt":"2020-10-01T01:22:00","guid":{"rendered":"https:\/\/mathvault.ca\/?p=31923"},"modified":"2022-05-17T21:15:28","modified_gmt":"2022-05-18T01:15:28","slug":"euler-formula","status":"publish","type":"post","link":"https:\/\/mathvault.ca\/euler-formula\/","title":{"rendered":"Euler’s Formula: A Complete Guide"},"content":{"rendered":"\n

In the world of complex numbers, as we integrate trigonometric expressions, we will likely encounter the so-called Euler\u2019s formula<\/strong>.<\/p>\n\n\n\n

Named after the legendary mathematician Leonhard Euler<\/a>, this powerful equation deserves a closer examination \u2014 in order for us to use it to its full potential.<\/p>\n\n\n\n

We will take a look at how Euler’s formula allows us to express complex numbers as exponentials<\/strong>, and explore the different ways it can be established with relative ease.<\/p>\n\n\n\n

In addition, we will also consider its several applications<\/strong> such as the particular case of Euler’s identity, the exponential form of complex numbers, alternate definitions of key functions, and alternate proofs of de Moivre\u2019s theorem<\/a> and trigonometric additive identities<\/a>.<\/p>\n\n\n

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Note<\/p>\n

This Euler’s formula is to be distinguished from other Euler’s formulas, such as the one for convex polyhedra<\/strong><\/a>.<\/p>\n<\/div>\n\n\n

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Prefer the PDF version instead?<\/p>\n

Get our complete, 22-page guide on Euler’s formula\u2014in offline, printable PDF format<\/strong>.<\/p>\n\n\n\n

Yes. That’d be great.<\/a><\/div><\/span>\n<\/div><\/div>\n<\/div><\/div>\n\n\n

\"Diagram<\/p>\n

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Table of Contents<\/p>\nToggle<\/span><\/path><\/svg><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n