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?