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Geometry/Logarithm and Antilogarithm of Complex Numbers.

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Question
Dear Prof Azeem

Can we compute the Logarithm and Antilogarithm of complex numbers?

Examples

Log(100+2i)
Antilog(2-3i)

Thanks
Prashant

Answer
Hi Prashant,

Yes we can, although there are infinitely many solutions to a complex logarithm, all separated by integer multiples of 2πi.  We must therefore be sure to define our logarithm properly (e.g. by specifying a branch cut).  Having done so, many of the logarithm rules on the real numbers still apply.

Thanks for asking,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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