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I am building an Eldritch Knight fighter/War wizard multiclass character for D&D 5e. The eldritch knight has a limited pool of spells known, but does not have to prepare them; the wizard, on the other hand, needs to prepare his spells each day.

Are the spells known from the Eldritch Knight part of my character and can be cast without preparing them? Or am I now stuck preparing spells like a normal wizard?

For example, as a level 3 Eldritch Knight I know 3 spells, and I do not have to prepare them to cast them. Then I take a level of wizard; as a 1st-level wizard, you get a spellbook containing 6 spells, and can only prepare a number of spells to be cast from this book equal to Int modifier + wizard level.

For example, if my character has an Intelligence score of 14, he could prepare 3 spells as a wizard, but he already knows 3 other spells from being an Eldritch Knight that don't need to be prepared to be cast, at least as far as I understand the rules.

Is my character now limited to preparing spells only, or does he keep his Eldritch Knight spells as always being able to be cast?

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    \$\begingroup\$ Very related (not a duplicate): Arcane Trickster Multiclass - Spell Preparation. @ElianisTheBrave: Since you believe you have your answer now, I'd suggest self-answering your question based on your understanding now that the question has been reopened. :) \$\endgroup\$ – V2Blast Jul 1 at 3:20
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The PHB (page 164) says the following for multiclassed casters:

You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.

This means that your spells known as an EK are separate from the spells in your wizard spell book. EK spells are known and can always be cast, wizard spells are in your spell book and must be prepared in order for you to cast them. The only way these classes affect each other is through spell slots. The rules state:

You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature. Use this total to determine your spell slots by consulting the Multiclass Spellcaster table.

So your 3 EK/1 Wizard would be considered a level 2 multiclassed spellcaster and have 3 1st level slots, as per the table in PHB.

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