P. Luckey's complex root finder

In an article about nomograms for finding complex roots of quadratic equations, P. Luckey describes a special slide rule for the same purpose.

Solve the equation z² + p z + q = 0 for complex number z = ζ + i η   (ζ and η are real numbers!)
This is equivalent to solving two equations:      
ζ² − η² + p ζ + q = 0 and 2 ζ η + p η = 0
Luckey's slide rule gives the values
d = √¼p² − q   and η = √q − ¼p²

Below you see a drawing of Luckey's slide rule, and its algorithm. Enter values for p and q, press Go and see what happens

z² + z + = 0    
Is q to the left of |p| ?
  ↓yes       ↓no  
Real roots Complex roots
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η = 0 ζ = −½p
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Slide the value of q under η = 0 Slide the value of |p| above 0
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Read d under |p| Read η above q
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The roots are −½p ± d The roots are −½p ± i η

In the original paper, ζ is used instead of d but this rather confusing: ¼p² − q is the square root of the discriminant-part of the (real) root, but not the complete (real) root, which is −½p ± √¼p² − q