(2-i)-standard-form.jpeg "(2+3i)(2-i) Standard Form")
Simplifying Complex Numbers: (2 + 3i)(2 - i)
This article will guide you through the process of simplifying the product of two complex numbers, (2 + 3i)(2 - i), and expressing the result in standard form.
Understanding Complex Numbers
A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, where i² = -1.
The standard form of a complex number is simply writing it in the form a + bi.
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property, just like we would with binomials.
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Expand the product: (2 + 3i)(2 - i) = 2(2 - i) + 3i(2 - i)
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Distribute: = 4 - 2i + 6i - 3i²
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Substitute i² = -1: = 4 - 2i + 6i + 3
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Combine real and imaginary terms: = (4 + 3) + (-2 + 6)i
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Simplify: = 7 + 4i
Conclusion
Therefore, the product of (2 + 3i)(2 - i) expressed in standard form is 7 + 4i.