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The problem you're solving involves dividing complex numbers:

\[
\frac{5 - 3i}{-2i}
\]

To divide complex numbers, we multiply the numerator and the denominator by the complex conjugate of the denominator. Since the denominator is \(-2i\), its complex conjugate is \(2i\). Let's follow the steps:

1. Multiply both numerator and denominator by \(2i\):

\[
\frac{(5 - 3i)(2i)}{-2i(2i)}
\]

2. Simplify the denominator first:

\[
-2i \cdot 2i = -4i^2 = -4(-1) = 4
\]

So the denominator becomes 4.

3. Now simplify the numerator:

\[
(5 - 3i)(2i) = 5(2i) - 3i(2i) = 10i - 6i^2
\]

Since \(i^2 = -1\), this simplifies further:

\[
10i - 6(-1) = 10i + 6
\]

So the numerator becomes \(6 + 10i\).

4. Now we divide the simplified numerator by the denominator:

\[
\frac{6 + 10i}{4} = \frac{6}{4} + \frac{10i}{4} = 1.5 + 2.5i
\]

Thus, the answer in standard form is:

\[
1.5 + 2.5i
\]

Let me know if you'd like further clarification on any step!

Here are 5 related questions you can explore:
1. How do you divide complex numbers with both real and imaginary parts in the denominator?
2. What is the significance of the complex conjugate when dividing complex numbers?
3. How do you multiply two complex numbers?
4. What is the geometric interpretation of dividing complex numbers?
5. How do you express the result of division in polar form?

**Tip:** Always simplify your denominator first when dividing complex numbers by multiplying by the conjugate to eliminate the imaginary part.

Divide (5 - 3i) by (-2i). Write your answer as a complex number in standard form.

Learn how to divide complex numbers with a step-by-step solution to the problem (5 - 3i) ÷ (-2i). This problem covers key concepts like complex conjugate multiplication and simplifying imaginary numbers. Suitable for high school students in Grades 10-12.

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