Question

5i·(5 + 3i) =
your answer should be a complex number in the form a + bi where a and b are real numbers.

Explanation:

Step1: Use distributive property (FOIL)

$5i \cdot (5 + 3i) = 5i \cdot 5 + 5i \cdot 3i$

Step2: Simplify each term

$5i \cdot 5 = 25i$, $5i \cdot 3i = 15i^2$

Step3: Recall $i^2 = -1$

$15i^2 = 15(-1) = -15$

Step4: Combine terms

$25i - 15 = -15 + 25i$

Answer:

$-15 + 25i$