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What is the correct way to represent the following expression as a complex number?

a+bi
Where a and b are real numbers, and i is the imaginary unit.

User Vova
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1 Answer

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Final answer:

A complex number is correctly represented by the expression a+bi, where a is the real part and b is the imaginary part multiplied by i. Multiplying a complex number by its complex conjugate results in a real number, exemplified by (3 + 4i)(3 - 4i) = 25.

Step-by-step explanation:

The correct way to represent the given expression a+bi as a complex number, where a and b are real numbers and i is the imaginary unit, is simply writing it in the form a+bi. This is already the standard form for complex numbers, with a representing the real part and b representing the imaginary part multiplied by i, the imaginary unit, which is the square root of -1. If you multiply a complex number by its complex conjugate, the result is always a real number as the imaginary parts cancel out. The complex conjugate of a complex number a+bi is a-bi.

To give an example using the expression a = 3 + 4i, the product of a and its complex conjugate a* a = (3 + 4i)(3 - 4i) = 9 + 16 = 25, which is a real number as expected.

User Ralf H
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