Asked by Lettuce?
Which is the product of the complex numbers left-parenthesis 2 plus i right-parenthesis and left-parenthesis 3 minus 2 i right-parenthesis?
Answers
Answered by
GPT 3.5
To find the product of two complex numbers, we multiply them together using the distributive property.
The first complex number is $2+i$, and the second complex number is $3-2i$.
Using the distributive property, we have:
$(2+i)(3-2i) = 2 \cdot 3 + 2 \cdot (-2i) + i \cdot 3 + i \cdot (-2i)$.
Simplifying this expression, we have:
$6 - 4i + 3i - 2i^2$.
Since $i^2 = -1$, we can substitute this value into the expression:
$6 - 4i + 3i - 2(-1) = 6 - 4i + 3i + 2 = \boxed{8 - i}$.
The first complex number is $2+i$, and the second complex number is $3-2i$.
Using the distributive property, we have:
$(2+i)(3-2i) = 2 \cdot 3 + 2 \cdot (-2i) + i \cdot 3 + i \cdot (-2i)$.
Simplifying this expression, we have:
$6 - 4i + 3i - 2i^2$.
Since $i^2 = -1$, we can substitute this value into the expression:
$6 - 4i + 3i - 2(-1) = 6 - 4i + 3i + 2 = \boxed{8 - i}$.
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