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Equality of fractions in $\mathbb{C}$

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#complex-numbers
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Prove that 4 points belong to the same circle by using complex numbers

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#calculus #linear-algebra #geometry #complex-numbers #circles
101
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If $z=\cos \theta + i \sin \theta$, express $\displaystyle \frac {1}{1-z \cos \theta}$ in the form $a+i\cdot b$.

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#complex-numbers
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Can someone confirm if my answer is right?( complex numbers)

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#complex-numbers
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Need help on last few steps of complex numbers

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#complex-numbers
433
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Find the values of all the cube roots of $\cos \pi + i \sin \pi$

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#complex-numbers
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A proof that eigenvalues of unitary matrix must be complex

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#complex-numbers #eigenvalues-eigenvectors #hilbert-spaces #eigenfunctions #unitary-matrices
40
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Complex conjugation

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#complex-numbers
209
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How do I show $\arccos(4)$ in form $a+bi$?

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#complex-numbers
67
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Is it possible to make a proper limit of $\ln x$ in $\mathbb{C}$

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#complex-analysis #limits #complex-numbers #logarithms #exponential-function
97
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A complex number $z_1$ is unimodular. If $\frac{z_1-2z_2}{2-z_1\bar z_2}$ is unimodular, and $z_2$ is not unimodular, then prove that....

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#complex-numbers
60
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Solve $(1+iz)^n=m(1-iz)^n$

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#trigonometry #complex-numbers
34
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How does: $−i2nπ∓iz=arccosh(4) $ lead to, $z=arccos(4)=2πn±iarccosh(4)?$

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#complex-numbers
41
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Find the locus of the complex number from the given data

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#complex-numbers
94
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Determining the locus of z where $|z-(2+i)|=|z|\sin(\pi/4-\arg(z))$

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#complex-analysis #complex-numbers #analytic-geometry #conic-sections #locus

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