Complex numbers: i, adding, multiplying, dividing
Meet the number i with iΒ² = β1, add complex numbers as points on the plane, multiply them like brackets and divide with the conjugate.
π Start here: read the steps of the βLessonβ in order (1, 2, 3 β¦) and answer each question. Then continue with βPracticeβ.
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Guide
The imaginary unit is i, with i2 = β1. A complex number is written a + bi: a is the real part and b is the imaginary part. On the complex plane the real part goes across and the imaginary part goes up, so 2 + 3i is the point 2 across and 3 up.
To add, add the real parts and add the imaginary parts. To multiply, expand the brackets, then replace i2 by β1.
To divide, multiply the top and the bottom by the conjugate of the bottom. The conjugate of a + bi is a β bi, and (a + bi)(a β bi) = a2 + b2 is a real number.