which formula should i use?

Back in the old days when engineers had drafting tools and knew how to use them, what we did to work with complex numbers was to plot them on polar graph paper (to facilitate conversion between rectangular & polar representations of complex numbers) and solve problems like this with about 2% (slide rule) accuracy.

So when given a problem in polar form (magnitude & phase) that requires the addition of complex numbers in rectangular form (real & imaginary), the best avenue for solution is to visualize the problem as a phasor diagram which helps to track the conversion of complex numbers between polar and rectangular representations. Because the answer to your question is to use the formulae to convert between the polar & rectangular form of complex numbers.

 

One motor draws 20 Ampere lamp and 15 Ampere current. The current drawn by the lamp is in phase with the voltage; The current drawn by the motor is 60 degrees ahead of the voltage. What is the total current value drawn by the motor and lamps from the network by considering the voltage as zero phase? (cos60 = 0,5)


can i find this question with Pythagorean Theorem ?

 

can i find this question with Pythagorean Theorem ?

You should use a phasor diagram, convert polar coordinates to rectangular, add the real & imaginary components, then convert back to polar coordinates to get the answer. Or if you are careful in drawing the phasor diagram, just measure the answer from the drawing.