I keep getting “Modulus and conjugate” questions wrong in Complex Numbers. What's the trap?
forgetting that z times its conjugate equals |z|² (a real number).
The usual trap: forgetting that z times its conjugate equals |z|² (a real number). How to avoid it: multiply by the conjugate to rationalise a complex denominator. Go back to the definition — the modulus |z|=√(a²+b²) is the distance from the origin; the conjugate of a+bi is a−bi.
Key point
Modulus and conjugate
Common mistake
forgetting that z times its conjugate equals |z|² (a real number).
Memory tip
multiply by the conjugate to rationalise a complex denominator.
Tap to watch or see it right here — the app stays open (it only opens a quick search if nothing embeddable is found).