Answer: a² + b².
- A a² - b²
- B 2ab
- C a² + b²
- D a + b
Correct answer: C. a² + b²
Explanation: z x z-bar = (a+ib)(a-ib) = a<sup>2</sup>+b<sup>2</sup> = |z|<sup>2.</sup>
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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