The problem shown is:

$(2 + 5i) \cdot (5 - 3i)$

To multiply these complex numbers, we'll use the distributive property (FOIL method).

Step-by-step solution:

1. Multiply the real and imaginary parts: $(2)(5) + (2)(-3i) + (5i)(5) + (5i)(-3i)$

2. Perform each multiplication:

   • $2 \cdot 5 = 10$
   • $2 \cdot (-3i) = -6i$
   • $5i \cdot 5 = 25i$
   • $5i \cdot (-3i) = -15i^2$

3. Simplify using $i^2 = -1$:

   • $-15i^2 = -15(-1) = 15$

4. Combine all the terms: $10 + (-6i) + 25i + 15$ Simplifies to: $(10 + 15) + (-6i + 25i) = 25 + 19i$

Final Answer:

$25 + 19i$

Would you like further clarification or details?

Related questions:

1. What is the general form of a complex number?
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4. What is the conjugate of a complex number and how is it used?
5. How do you find the magnitude of a complex number?

Tip:

When multiplying complex numbers, remember to simplify $i^2$ as $-1$ to get a real number.