Question

What is the product of the complex numbers 3 − 4 � 3−4i3, minus, 4, i and − 6 + � −6+iminus, 6, plus, i, where � = − 1 i= −1 ​ i, equals, square root of, minus, 1, end square root ? Choose 1 answer: − 22 + 27 � −22+27iminus, 22, plus, 27, i − 18 − 3 � −18−3iminus, 18, minus, 3, i − 14 + 27 � −14+27iminus, 14, plus, 27, i − 3 − 3 � −3−3iminus, 3, minus, 3, i

Answer 1

Step-by-step explanation:

AI-generated answer

To find the product of complex numbers, we can use the distributive property and simplify the expression. Let's break down the given expression step by step:

First, let's simplify the complex numbers:

3 - 4i = 3 + (-4i)

-6 + i = -6 + 1i

Now, let's find the product of these complex numbers:

(3 + (-4i))(3 - 4i) = 3(3) + 3(-4i) + (-4i)(3) + (-4i)(-4i)

= 9 - 12i - 12i + 16i^2

Next, let's simplify the product:

i^2 is defined as -1, so:

= 9 - 12i - 12i + 16(-1)

= 9 - 12i - 12i - 16

= -7 - 24i

Finally, let's multiply this result by -6 + i:

(-7 - 24i)(-6 + i) = (-7)(-6) + (-7)(i) + (-24i)(-6) + (-24i)(i)

= 42 - 7i + 144i + 24

= 66 + 137i

Therefore, the product of the given complex numbers is 66 + 137i.