Picture complex numbers as points, find their modulus and conjugate and what they mean on the plane, then solve quadratic equations with a negative discriminant and find square roots of complex numbers.
3 lessons, about 1 h 15 min3 simulations12 problems3 practice questionsPython in every lesson
Created by StemPy LabThe conjugate of is , and its modulus is . The two are linked by . Conjugates pass through sums and products, moduli multiply, and the conjugate turns any division into a multiplication.
The number is the point of the Argand plane, with real numbers on the horizontal axis and purely imaginary ones on the vertical axis. The modulus is the distance from the origin. The conjugate is the mirror image in the real axis. The distance between and is .
A quadratic with real coefficients and a negative discriminant has two complex roots, . They are conjugates of each other, so they are mirror images on the Argand plane. The square roots of come from solving .
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