MATL, 7 bytes

BJ*Y'^s

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###How it works

Consider input 4538 for example.

B % Implicit input. Convert to binary
 % STACK: [1 0 0 0 1 1 0 1 1 1 0 1 0]
J* % Multiply by 1i
 % STACK: [1i 0 0 0 1i 1i 0 1i 1i 1i 0 1i 0]
Y' % Run-length encoding
 % STACK: [1i 0 1i 0 1i 0 1i 0], [1 3 2 1 3 1 1 1]
^ % Power, element-wise
 % STACK: [1i 0 -1 0 -1i 0 1i 0]
s % Sum of array. Implicit display
 % STACK: -1+1i

MATL, 7 bytes

BJ*Y'^s

Try it online!

How it works

Consider input 4538 for example.

B % Implicit input. Convert to binary
 % STACK: [1 0 0 0 1 1 0 1 1 1 0 1 0]
J* % Multiply by 1i
 % STACK: [1i 0 0 0 1i 1i 0 1i 1i 1i 0 1i 0]
Y' % Run-length encoding
 % STACK: [1i 0 1i 0 1i 0 1i 0], [1 3 2 1 3 1 1 1]
^ % Power, element-wise
 % STACK: [1i 0 -1 0 -1i 0 1i 0]
s % Sum of array. Implicit display
 % STACK: -1+1i

MATL, 7 bytes

BJ*Y'^s

Try it online!

###How it works

B % Implicit input. Convert to binary
J* % Multiply by 1i
Y' % Run-length encoding
^ % Power, element-wise
s % Sum of array. Implicit display

MATL, 7 bytes

BJ*Y'^s

Try it online!

###How it works

Consider input 4538 for example.

B % Implicit input. Convert to binary
 % STACK: [1 0 0 0 1 1 0 1 1 1 0 1 0]
J* % Multiply by 1i
 % STACK: [1i 0 0 0 1i 1i 0 1i 1i 1i 0 1i 0]
Y' % Run-length encoding
 % STACK: [1i 0 1i 0 1i 0 1i 0], [1 3 2 1 3 1 1 1]
^ % Power, element-wise
 % STACK: [1i 0 -1 0 -1i 0 1i 0]
s % Sum of array. Implicit display
 % STACK: -1+1i