Meet i, write numbers as a + ib, and add, subtract, multiply and divide them. Find powers of i, and the identities that still hold for complex numbers.
3 lessons, about 1 h 15 min3 simulations10 problems5 practice questionsPython in every lesson
Created by StemPy LabThe square of a real number is never negative, so has no real root. We bring in a new number with . Then for every positive . A complex number is , with real part and imaginary part . Two complex numbers are equal only when both parts are equal.
Add or take away complex numbers part by part: real with real, imaginary with imaginary. Multiply them like brackets in algebra, and put for : . The operations keep the familiar properties: closure, commutative and associative laws, the identities and , and the distributive law. Identities such as still hold.
To divide by , multiply the top and the bottom by : the bottom becomes the real number . Every non-zero complex number has the multiplicative inverse . The powers of repeat in a cycle of four: . So depends only on the remainder of on division by . The rule fails when and are both negative.
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