RLC

Hello All
Say I have a resistor R, inductor L and capacitor C connected together
in series

The easiest way to find the total impedance is just plug the formula
a+ bj

Z= square root (a^2 + b^2 )

without drawing any phasor diagram right?

For example
R + Xc + XL = R + jwL - (j /wC)
= R + j (wL - (1/wC)
= a + j b

so Z total is square root( a^2 + b^2 )

Am I right?

Can I always plug in equation square root( a^2 + b^2 ) without drawing
a phasor diagram?
If cannot what is the reason and any example to explain it?

Kindly enlighthen

Thank you


Jason

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