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Find z̄ × z (where z = a + ib):

Aa² + b² = |z|²
B2a
Ca² - b²
D|z|
Answer & Solution
Correct answer: A. a² + b² = |z|²
We have z × z̄ = (a + ib)(a - ib). That is z × z̄ = a² - (ib)². That is z × z̄ = a² + b². So z × z̄ = |z|². **So conjugate times itself gives modulus squared.**
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