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The Number That Turned Sideways
A complex number comes in pairs: $a + bi$, where $a$ and $b$ are real numbers and $i$ is the square root of negative one. The magnitude is$$|z| = \sqrt{a^2 + b^2}$$ Given the magnitude and an angle $\theta$, you can reconstruct the number:$$z = |z|(\cos\theta + i\sin\theta)$$ These numbers are two-dimensional, like fractions — defined by two pieces of information.
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