Question

What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$?

score 306 · Answer 1 · 2026-03-25 22:26:52

306

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What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$?

Published on 25 Mar 2026 - 22:26

score 233 · Answer 2 · 2018-07-23 11:36:00

If $|z_1\pm z_2\pm\ldots\pm z_n|\le|w_1\pm w_2\pm\ldots\pm w_n|$, prove that $|z_1|^2+|z_2|^2+\ldots+|z_n|^2\le|w_1|^2+|w_2|^2+\ldots+|w_n|^2$.

score 2.5k · Answer 3 · 2018-07-23 12:17:10

2.5k

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101

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97

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score 1.5k · Answer 7 · 2018-07-26 04:51:32

1.5k

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score 94 · Answer 8 · 2026-03-25 18:43:46

94

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score 107 · Answer 9 · 2018-07-26 15:50:17

107

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score 623 · Answer 10 · 2026-03-25 09:33:22

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score 1.9k · Answer 12 · 2018-07-27 10:17:07

Find the area of the polygon whose vertices are the solutions in the complex plane of the equation $x^7+x^6+x^5+x^4+x^3+x^2+x+1=0$

score 54 · Answer 13 · 2018-07-27 10:27:24

54

Views

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score 67 · Answer 14 · 2018-07-27 11:32:52

67

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score 78 · Answer 15 · 2018-07-27 15:58:37

78

Views

Find all solutions $z^2\overline{z}^3=32$

Published on 27 Jul 2018 - 15:58

List Question

What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$?

If $|z_1\pm z_2\pm\ldots\pm z_n|\le|w_1\pm w_2\pm\ldots\pm w_n|$, prove that $|z_1|^2+|z_2|^2+\ldots+|z_n|^2\le|w_1|^2+|w_2|^2+\ldots+|w_n|^2$.

Raising complex number to high power - Cartesian form

How to subtract complex numbers in polar form?

Wrong implication in Complex number

Solve $| \frac{2+z}{2-z} | < 1$

Prove that all the roots of the equation $(1+z)^6+z^6=0$ are collinear.

Factorising complex numbers

Prove that all three roots of $f(x)=0$ are zero. Also prove that $a+b+c=0$.

Does Transpose preserve eigenvalues over the complex field?

Baby Rudin 1.14 is essentially Thales's theorem?

Find the area of the polygon whose vertices are the solutions in the complex plane of the equation $x^7+x^6+x^5+x^4+x^3+x^2+x+1=0$

Find out the condition for $k$ such that the locus of $z$ is a circle.

how to prove the below statement

Find all solutions $z^2\overline{z}^3=32$

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