The Imaginary Unit i
Aligned to N-CN.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
There is a number i defined by i^2 = −1, so i = √(−1). Every complex number can be written as a + bi, where a is the real part and b is the imaginary part, both real numbers.
Worked example
Write √(−25) in the form a + bi. Split it as √(25) × √(−1) = 5 × i = 5i. So √(−25) = 0 + 5i, with real part 0 and imaginary part 5.
Practice questions
- Write √(−49) in the form a + bi.
- Identify the real and imaginary parts of 3 − 7i.
- Express √(−16) + 2 as a complex number a + bi.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
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La Unidad Imaginaria i
Existe un número i definido por i^2 = −1, así que i = √(−1). Todo número complejo se puede escribir como a + bi, donde a es la parte real y b es la parte imaginaria, ambas números reales.
Ejemplo: Escribe √(−25) en la forma a + bi. Sepáralo como √(25) × √(−1) = 5 × i = 5i. Así que √(−25) = 0 + 5i, con parte real 0 y parte imaginaria 5.
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