(-5+3i)/(2i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (-5 + 3i) / (2i)

This article will guide you through the process of simplifying the complex number expression (-5 + 3i) / (2i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as √-1.

Simplifying the Expression

To simplify the expression (-5 + 3i) / (2i), we need to get rid of the imaginary number in the denominator. We can achieve this by multiplying both the numerator and denominator by the complex conjugate of the denominator.

The complex conjugate of 2i is -2i.

Here are the steps:

1. Multiply the numerator and denominator by the complex conjugate of the denominator:

   (-5 + 3i) / (2i) * (-2i) / (-2i)

2. Expand the multiplication:

   (10i - 6i²) / (-4i²)

3. Substitute i² with -1:

   (10i + 6) / 4

4. Rearrange to standard complex number form (a + bi):

   (3/2) + (5/2)i

Result

Therefore, the simplified form of (-5 + 3i) / (2i) is (3/2) + (5/2)i.