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Unformatted text preview: mbers Complex Conjugates
The complex conjugate of a + bi is the complex number
a − bi .
Observe what happens when we multiply a complex number
by its conjugate:
(a + bi )(a − bi ) = a2 − abi + abi − bi 2 = a2 + b 2 .
In particular, the product of complex conjugates is a real
(a + bi )(a − bi ) = a2 + b 2
1 Multiply 1 + i and its conjugate. 2 Multiply 4 − 3i and its conjugate. Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Numbers Dividing Complex Numbers
When we divide a + bi by c + di , we get a number of the form:
a + bi
c + di
This is a complex number!
We put it in standard form by multiplying numerator and
denominator by c − di (the complex conjugate of the
denominator) and simplifying.
1 Divide 2 + i by 1 − 3i , then put the result in standard form. 2 Divide −4 + 8i by 2 − 4i , then put the result in standard form....
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