%2B5i(1-3i)-in-standard-form.jpeg "(2-3i)+5i(1-3i) In Standard Form")
Simplifying Complex Numbers: (2-3i) + 5i(1-3i)
This article will guide you through the process of simplifying the complex number expression (2-3i) + 5i(1-3i) and expressing it in standard form.
Understanding Complex Numbers
Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).
Simplifying the Expression
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Distribute: Begin by distributing the 5i in the second term: (2-3i) + 5i(1-3i) = (2-3i) + (5i - 15i²)
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Substitute i²: Replace i² with -1: (2-3i) + (5i - 15(-1))
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Combine Real and Imaginary Terms: Combine the real terms (2 and 15) and the imaginary terms (-3i and 5i): (2 + 15) + (-3 + 5)i
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Simplify: Combine the terms to get the final result in standard form: 17 + 2i
Standard Form
A complex number is in standard form when it is expressed as a + bi, where a and b are real numbers. In our case, 17 + 2i is the simplified form of the complex number expression (2-3i) + 5i(1-3i).