Question

Show that $|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2|z_1|^2 + 2|z_2|^2$. Find a corresponding result for a finite set $\{z_1,z_2,\ldots,z_n\}$.

score 80 · Answer 1 · 2026-04-16 22:55:25

80

Views

Show that $|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2|z_1|^2 + 2|z_2|^2$. Find a corresponding result for a finite set $\{z_1,z_2,\ldots,z_n\}$.

Published on 16 Apr 2026 - 22:55

score 418 · Answer 2 · 2026-04-14 14:42:50

418

Views

Using sum-to-product formula to solve $\sin(2\theta)+\sin(4\theta)=0$

Published on 14 Apr 2026 - 14:42

score 134 · Answer 3 · 2026-04-10 18:35:48

134

Views

Giving an example of a strictly monotone function which is not injective.

Published on 10 Apr 2026 - 18:35

score 52 · Answer 4 · 2026-04-15 20:12:47

Suppose $a,b\in \mathbb{Z}$ are relatively prime and $c\in \mathbb{N}$ is a divisor of $a+b$. **Verify my proof** that gcd$(a,c)$=gcd$(b,c)=1$.

score 51 · Answer 5 · 2026-04-14 02:13:39

51

Views

Suppose that $(z_{n})_{n=1}^{\infty}$ converges to $z$. Show that $\overline{z}_{n}\to\overline{z}$ and $|z_{n}|\to |z|$ as $n\to\infty$.

Published on 14 Apr 2026 - 2:13

score 59 · Answer 6 · 2026-04-17 02:08:17

59

Views

Unboundedness of anti-derivative

Published on 17 Apr 2026 - 2:08

score 105 · Answer 7 · 2026-04-16 14:24:28

105

Views

Find all integers such that $\sqrt{(n-4)\sqrt{n-19}}$ is also an integer.

Published on 16 Apr 2026 - 14:24

score 458 · Answer 8 · 2026-04-15 16:15:45

458

Views

If any finite subcollection of finite sets has non-empty intersection, then the infinite intersection is non-empty as well.

Published on 15 Apr 2026 - 16:15

score 405 · Answer 9 · 2026-04-09 14:54:20

405

Views

Prove that none of the integers $11,111,1111,...$ are squares of an integer.

Published on 09 Apr 2026 - 14:54

score 1.3k · Answer 10 · 2026-04-13 21:05:34

1.3k

Views

X is Hausdorff iff a net converges to at most one point

Published on 13 Apr 2026 - 21:05

score 92 · Answer 11 · 2026-04-10 18:02:11

92

Views

Fixed Point theorem with Lipschitz continuous mapping.

Published on 10 Apr 2026 - 18:02

score 304 · Answer 12 · 2026-03-25 09:28:18

304

Views

Proof of Profinite groups are inverse limits of finite groups

Published on 25 Mar 2026 - 9:28

score 88 · Answer 13 · 2026-04-16 18:19:32

88

Views

How many baskets of n fruits can be formed that contains at most 3 apples, even number of pears, and any number of oranges and plums?

Published on 16 Apr 2026 - 18:19

score 1.4k · Answer 14 · 2026-04-11 06:07:47

1.4k

Views

How to prove that nth root of n is irrational

Published on 11 Apr 2026 - 6:07

score 341 · Answer 15 · 2026-04-18 02:25:21

341

Views

$f^{-1}(D-C)=f^{-1}(D)-f^{-1}(C)$

Published on 18 Apr 2026 - 2:25

List Question

Show that $|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2|z_1|^2 + 2|z_2|^2$. Find a corresponding result for a finite set $\{z_1,z_2,\ldots,z_n\}$.

Using sum-to-product formula to solve $\sin(2\theta)+\sin(4\theta)=0$

Giving an example of a strictly monotone function which is not injective.

Suppose $a,b\in \mathbb{Z}$ are relatively prime and $c\in \mathbb{N}$ is a divisor of $a+b$. Verify my proof that gcd$(a,c)$=gcd$(b,c)=1$.

Suppose that $(z_{n})_{n=1}^{\infty}$ converges to $z$. Show that $\overline{z}_{n}\to\overline{z}$ and $|z_{n}|\to |z|$ as $n\to\infty$.

Unboundedness of anti-derivative

Find all integers such that $\sqrt{(n-4)\sqrt{n-19}}$ is also an integer.

If any finite subcollection of finite sets has non-empty intersection, then the infinite intersection is non-empty as well.

Prove that none of the integers $11,111,1111,...$ are squares of an integer.

X is Hausdorff iff a net converges to at most one point

Fixed Point theorem with Lipschitz continuous mapping.

Proof of Profinite groups are inverse limits of finite groups

How many baskets of n fruits can be formed that contains at most 3 apples, even number of pears, and any number of oranges and plums?

How to prove that nth root of n is irrational

$f^{-1}(D-C)=f^{-1}(D)-f^{-1}(C)$

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