Answer: p² = q.
- A p = 0
- B p² = q
- C q must be maximum
- D p must equal q
Correct answer: B. p² = q
Explanation: r² + s² = (r+s)² - 2rs = 4p² - 2q. Minimize means dL/dq = -2 < 0 so max q, but constraint D = 4p² - 4q ≥ 0 means q ≤ p². Minimum r²+s² at boundary q = p².
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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