Question

watch the video and then solve the problem given below.
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find the following product and write the result in standard form, (a + bi).
((-4 + 5i)(9 + i))

Explanation:

Step1: Expand using distributive property

$(-4)(9) + (-4)(i) + (5i)(9) + (5i)(i)$

Step2: Calculate each term

$-36 - 4i + 45i + 5i^2$

Step3: Substitute $i^2=-1$

$-36 - 4i + 45i + 5(-1)$

Step4: Simplify real terms

$-36 -5 - 4i + 45i$

Step5: Combine like terms

$-41 + 41i$

Answer:

$-41 + 41i$