# How to rotate a list of imaginary points

**URL:** <https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731>\
**Category:** Questions\
**Tags:** desmos-calculator\
**Created:** [May 29, 2026, 12:33pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731 "2026-05-29T12:33:58Z")\
**Posts on this page:** 12\
**Page:** 1

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**Author:** ![port](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/port/32/9839_2.png) [@port](https://cl.desmos.com/u/port)\
**Post date:** [May 29, 2026, 12:33pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/1 "2026-05-29T12:33:58Z")

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When you have a list of complex points that you have not defined yourself such as (.1+.1i)^[1…10], is there a way to rotate said points?

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**Author:** ![Guzman\_Tierno](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/guzman_tierno/32/6149_2.png) [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)\
**Post date:** [May 29, 2026, 2:19pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/2 "2026-05-29T14:19:34Z")

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rotation in complex numbers is just multiplication …  
if you want to rotate by 90° degrees you multiply times _i_  
and in general if you want to rotate by alpha degrees (in radiants)  
you multiply times e^(i\*alpha).

So in your situation:  
`e^(alpha*i) * (.1+.1i)^[1…10]`

where alpha is the angle or rotation you want in radiants.

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<div class="post-metadata">

**Author:** ![port](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/port/32/9839_2.png) [@port](https://cl.desmos.com/u/port)\
**Post date:** [May 29, 2026, 2:22pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/3 "2026-05-29T14:22:55Z")

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what about around a certain point?

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<div class="post-metadata">

**Author:** ![Guzman\_Tierno](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/guzman_tierno/32/6149_2.png) [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)\
**Post date:** [May 29, 2026, 2:25pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/4 "2026-05-29T14:25:20Z")

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if you want to rotate the complex number c around point p of angle alpha  
you just do this:

p + e^(alpha i) \* (c-p)

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<div class="post-metadata">

**Author:** ![Guzman\_Tierno](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/guzman_tierno/32/6149_2.png) [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)\
**Post date:** [May 29, 2026, 2:26pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/5 "2026-05-29T14:26:49Z")

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here:  
[https://www.desmos.com/calculator/bmqktsfpnx](https://www.desmos.com/calculator/bmqktsfpnx)

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<div class="post-metadata">

**Author:** ![port](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/port/32/9839_2.png) [@port](https://cl.desmos.com/u/port)\
**Post date:** [May 29, 2026, 2:27pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/6 "2026-05-29T14:27:27Z")

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this is helpful, thank you

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<div class="post-metadata">

**Author:** ![Guzman\_Tierno](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/guzman_tierno/32/6149_2.png) [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)\
**Post date:** [May 29, 2026, 2:34pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/7 "2026-05-29T14:34:56Z")

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What are you programming? Sunflower seeds?

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<div class="post-metadata">

**Author:** ![port](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/port/32/9839_2.png) [@port](https://cl.desmos.com/u/port)\
**Post date:** [May 29, 2026, 2:37pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/8 "2026-05-29T14:37:01Z")

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something with this: [Complex Numbers](https://cl.desmos.com/t/complex-numbers/8705/)

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<div class="post-metadata">

**Author:** ![Guzman\_Tierno](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/guzman_tierno/32/6149_2.png) [@Guzman\_Tierno](https://cl.desmos.com/u/Guzman_Tierno)\
**Post date:** [May 29, 2026, 2:39pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/9 "2026-05-29T14:39:18Z")

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you made me think about this possibility:  
[https://www.desmos.com/calculator/e7960b66ae](https://www.desmos.com/calculator/e7960b66ae)

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**Author:** ![Daniel\_Grubbs](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/daniel_grubbs/32/719_2.png) [@Daniel\_Grubbs](https://cl.desmos.com/u/Daniel_Grubbs)\
**Post date:** [May 29, 2026, 3:06pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/10 "2026-05-29T15:06:03Z")

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That was too much! LOL I had to slow the sliders down to 0.2x. That’s cool.

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<div class="post-metadata">

**Author:** ![port](https://yyz1.discourse-cdn.com/flex031/user_avatar/cl.desmos.com/port/32/9839_2.png) [@port](https://cl.desmos.com/u/port)\
**Post date:** [May 29, 2026, 3:17pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/11 "2026-05-29T15:17:13Z")

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this was weirdly hypnotizing

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<div class="post-metadata">

**Author:** ![system](https://canada1.discourse-cdn.com/flex031/uploads/desmos/original/2X/f/f5bd144684474e9a2f333002cde9840e52c5dbd3.png) [@system](https://cl.desmos.com/u/system)\
**Post date:** [May 31, 2026, 3:17pm UTC](https://cl.desmos.com/t/how-to-rotate-a-list-of-imaginary-points/8731/12 "2026-05-31T15:17:58Z")

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