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If z=a+bi then f(z)=f(a+bi)=$e^{a+bi}=e^{a}e^{bi}$. For each of the following complex number find...

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#complex-analysis #complex-numbers
998
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Conjugate quadratic equations

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#complex-numbers #quadratics
90
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Complex numbers - prove |BD| + |CD| = |AD|

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#geometry #complex-numbers #euclidean-geometry #circles #triangles
4.4k
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Proving that a complex number is real

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#complex-numbers
523
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Prove or disprove that Arg(zw)=Arg(z)+Arg(w)

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#complex-analysis #complex-numbers
48
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Proof for f must be a constant polynomial

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#complex-analysis #proof-verification #complex-numbers #partial-derivative #proof-explanation
107
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Rewrite Matrix such that it has only real eigenvalues

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#matrices #complex-numbers #eigenvalues-eigenvectors
114
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How to prove that $\frac{1-z}{|1-z|}$ is a root of unity with $z=e^{i\frac{2\pi}{n}}$

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#complex-analysis #algebra-precalculus #complex-numbers #finite-groups
93
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Complex numbers in programming

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#complex-numbers #fourier-transform
78
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Please, explain this problem to me, I got lost at the step where they turned the denominator into 1

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#complex-numbers
193
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Show that if $|a|=1$ or $|b|=1$, then $\left|\dfrac{a-b}{1-\overline{a}b}\right|\leq 1$

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#algebra-precalculus #complex-numbers
1.1k
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Triangle in complex plane

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#complex-analysis #complex-numbers
49
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Can anyone show that this equation is true?

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#complex-numbers
707
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Polynomial Equation Problem with Complex Roots

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#complex-numbers #quadratics #radicals #substitution #cubics
326
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Show that $|\text{Re}(2+3z^2 +iz)| \leq 6$, when $|z|\leq 1$

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#inequality #complex-numbers

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