Question

What is $[\cos(\pi/12)+i\sin(\pi/12)]^{16}+[\cos(\pi/12)-i\sin(\pi/12)]^{16}$?

score 536 · Answer 1 · 2018-08-26 11:44:03

536

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What is $[\cos(\pi/12)+i\sin(\pi/12)]^{16}+[\cos(\pi/12)-i\sin(\pi/12)]^{16}$?

Published on 26 Aug 2018 - 11:44

score 85 · Answer 2 · 2018-08-26 21:21:45

85

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Proving that $\sqrt{2} |z| \geq |x| + |y|$ for $z = x + iy$

Published on 26 Aug 2018 - 21:21

score 66 · Answer 3 · 2018-08-26 23:13:22

66

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Difference (or lack thereof) of the minus sign in complex exponentials in Fourier series

Published on 26 Aug 2018 - 23:13

score 296 · Answer 4 · 2026-03-25 17:45:32

296

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How do I expand $|z_{1} - z_{2}|^2$?

Published on 25 Mar 2026 - 17:45

score 1.5k · Answer 5 · 2018-08-28 10:31:57

1.5k

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$\sin(z)=0$ periodic of $2k\pi$ or $k\pi$?

Published on 28 Aug 2018 - 10:31

score 268 · Answer 6 · 2018-08-28 13:05:19

268

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complex exponential equation $e^{jz\pi}+j=0$

Published on 28 Aug 2018 - 13:05

score 56 · Answer 7 · 2018-08-28 16:50:17

56

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What does this inequality mean?

Published on 28 Aug 2018 - 16:50

score 67 · Answer 8 · 2018-08-28 21:40:24

67

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Proving that $\DeclareMathOperator{\Re}{Re}\DeclareMathOperator{\Im}{Im}|e^{z^2}| = e^{(\Re z)^2-(\Im z)^2}$

Published on 28 Aug 2018 - 21:40

score 351 · Answer 9 · 2018-08-28 22:40:13

351

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Proving $\DeclareMathOperator{\Re}{Re}\DeclareMathOperator{\Im}{Im}\Re{(\cosh z}) = \cosh(\Re z)\cdot \cos(\Im z)$

Published on 28 Aug 2018 - 22:40

score 209 · Answer 10 · 2018-08-29 04:18:39

209

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Can we compute $(-1)^{\frac{1}{2}}+(-1)^{\frac{1}{2}}?$

Published on 29 Aug 2018 - 4:18

score 2.1k · Answer 11 · 2018-08-29 12:34:26

2.1k

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Prove $\ \frac{z-1}{z+1} $ is imaginary no' iff $\ |z| = 1 $

Published on 29 Aug 2018 - 12:34

score 1.7k · Answer 12 · 2018-08-29 14:31:32

1.7k

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Converting complex numbers into Cartesian Form 3

Published on 29 Aug 2018 - 14:31

score 78 · Answer 13 · 2026-03-31 20:57:10

78

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prove the equation using complex numbers

Published on 31 Mar 2026 - 20:57

score 70 · Answer 14 · 2018-08-29 18:11:00

70

Views

Can Fermat's last theorem be proven false with complex numbers?

Published on 29 Aug 2018 - 18:11

score 2.1k · Answer 15 · 2018-08-29 20:55:57

2.1k

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Given that $z=\cos\theta+i\sin\theta$, show that $Re\left(\frac{z-1}{z+1}\right)=0, \quad z\ne-1$

Published on 29 Aug 2018 - 20:55

List Question

What is $[\cos(\pi/12)+i\sin(\pi/12)]^{16}+[\cos(\pi/12)-i\sin(\pi/12)]^{16}$?

Proving that $\sqrt{2} |z| \geq |x| + |y|$ for $z = x + iy$

Difference (or lack thereof) of the minus sign in complex exponentials in Fourier series

How do I expand $|z_{1} - z_{2}|^2$?

$\sin(z)=0$ periodic of $2k\pi$ or $k\pi$?

complex exponential equation $e^{jz\pi}+j=0$

What does this inequality mean?

Proving that $\DeclareMathOperator{\Re}{Re}\DeclareMathOperator{\Im}{Im}|e^{z^2}| = e^{(\Re z)^2-(\Im z)^2}$

Proving $\DeclareMathOperator{\Re}{Re}\DeclareMathOperator{\Im}{Im}\Re{(\cosh z}) = \cosh(\Re z)\cdot \cos(\Im z)$

Can we compute $(-1)^{\frac{1}{2}}+(-1)^{\frac{1}{2}}?$

Prove $\ \frac{z-1}{z+1} $ is imaginary no' iff $\ |z| = 1 $

Converting complex numbers into Cartesian Form 3

prove the equation using complex numbers

Can Fermat's last theorem be proven false with complex numbers?

Given that $z=\cos\theta+i\sin\theta$, show that $Re\left(\frac{z-1}{z+1}\right)=0, \quad z\ne-1$

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