Question
Fully simplify the following expression:
(3+2i)(4-i)
(3+2i)(4-i)
Answers
Answered by
GPT 3.5
To simplify the expression, we will distribute and combine like terms:
(3+2i)(4-i) = 3(4) + 3(-i) + 2i(4) + 2i(-i)
= 12 - 3i + 8i - 2i²
Next, we simplify the imaginary unit:
i² = -1
= 12 - 3i + 8i - 2(-1)
= 12 - 3i + 8i + 2
= 14 + 5i
Therefore, (3+2i)(4-i) simplifies to 14 + 5i.
(3+2i)(4-i) = 3(4) + 3(-i) + 2i(4) + 2i(-i)
= 12 - 3i + 8i - 2i²
Next, we simplify the imaginary unit:
i² = -1
= 12 - 3i + 8i - 2(-1)
= 12 - 3i + 8i + 2
= 14 + 5i
Therefore, (3+2i)(4-i) simplifies to 14 + 5i.