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Determinant of an identity matrix multiplied by a unit complex number

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#linear-algebra #complex-numbers
719
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How to algebraically calculate exact value of a trig function applied to any non-transcendental angle?

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#trigonometry #complex-numbers #analytic-geometry #angle
49
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If $a_k=\cos(2k\pi/n)-2+i\sin(2k\pi/n)$, evaluate $a_1a_2\cdots a_n$

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#trigonometry #complex-numbers
39
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Why does $\mathrm{exp}(i\mathbb R)$ produce the unit sphere of the 2-Norm?

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#complex-numbers #exponential-function #normed-spaces
293
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Do complex conjugates commute?

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#integration #complex-numbers #quantum-mechanics
220
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Inverse of a complex number in finite field

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#complex-numbers #finite-fields #inverse
24
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Complex series problem (basic complex variables)

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#complex-analysis #complex-numbers
96
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Argument principle for non-compact domains

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#complex-analysis #analysis #complex-numbers #complex-integration
60
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Change coordinate systems in for complex numbers

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#complex-numbers #coordinate-systems #spherical-coordinates
258
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Why does the difference equation $x_nx_{n+2}=w^5x_n-(w^2+w^3)x_{n+1}+x_{n+2}$ generate cyclic sequences?

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#complex-numbers #recurrence-relations
26
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Finding corresponding eigenvectors for complex matrix

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#linear-algebra #complex-numbers #eigenvalues-eigenvectors
223
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Drawing a Circle in the Complex Plane from a Polynomial

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#polynomials #complex-numbers
123
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Positivity of a complex-valued inner product

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#linear-algebra #complex-numbers #vector-spaces #inner-products
67
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Closure of a set of complex numbers

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#complex-analysis #complex-numbers #metric-spaces
162
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For a regular polygon with n edges, Is $z_k^n=1$?

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#complex-numbers #polar-coordinates

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