Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

5. Given complex numbers $z_{1}, z_{2}$ satisfy $\left|z_{1}\right| \geqslant 1,\left|z_{2}\right| \geqslant \frac{3}{2}$ . Then the minimum value of the modulus of the complex number $i^{1993} z_{1}+i^{1995} z_{2}+2 z_{1} z_{2}$ is $\qquad$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

5. $\frac{1}{2}$

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