What is the use/need of complex numbers in real life if they are imaginary?
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They are actually essential to modern physics and engineering.
“Imaginary” is just a name that appeared historically when these ‘weird’ (at the time) numbers were invented, and now we’re stuck with it. But complex numbers appear in fundamental physics, e.g. within quantum [wave functions](https://en.wikipedia.org/wiki/Wave_function), mathematical objects that are used along with [Schrödinger’s equation](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Time-dependent_equation) which describes the behavior of a quantum object through time. It’s really weird that “non-real” quantities appear when trying to describe an actual, entirely real object, but it’s the most natural way to express these equations.
Linear algebra can be used to replace complex numbers with matrices, but :
* matrix multiplication works in such a convoluted way (in relation to usual number multiplication) that it does not feel as if you’re actually manipulating the ‘true’ physics
* the matrices that are used in these kinds of expressions actually *are* (in a [mathematical kind of way](https://en.wikipedia.org/wiki/Isomorphism)) complex numbers anyway.
Complex numbers are also widely use to simplify calculations when it *is* possible to do without them, but doing so would make things much more complicated. For instance, a signal `s(t)`, which depends on time, can be expressed as `s(t)=R×e^(iθ)` where `R` is a real *amplitude* and `θ` is a real *phase*, usually between 0 and 2π.
If you represent `s(t)` as an arrow, the `e^(iθ)` term is a complex phase component that describes which direction the arrow is pointing, whereas `R` describes its length. You can now make it so θ depends on time, and now `s(t)=R×e^i(θ(t))` is a signal whose amplitude does not vary, but whose phase does. Which, for instance, is the behavior of electric and magnetic fields in most (arguably simplified) cases!
This is also useful because taking the derivative of a signal with respect to time can be expressed with complex numbers as simply multiplying it by `iω`, where ω is the signal’s pulse (in rad/s). This hugely simplifies calculations. In order to retrieve the ‘real’ signal, you then simply take the real part of your complex signal.
However, taking the real part of a wave function (in quantum mechanics such as mentioned earlier) does not ‘mean’ anything, which is why I used that as an example of complex numbers appearing in a fundamental way.
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