Fully simplify the following expression:
(3+2i)(4-i)
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.
To simplify the expression (3+2i)(4-i), we will use the distributive property of multiplication.
First, we multiply the real parts of the two complex numbers:
(3)(4) = 12
Next, we multiply the imaginary parts of the two complex numbers:
(3)(-i) = -3i
(2i)(4) = 8i
Now, we combine the real and imaginary parts to form the simplified expression:
12 + (-3i) + 8i
Finally, we combine like terms:
12 + 5i
Therefore, the fully simplified expression is 12 + 5i.
To fully simplify the expression (3+2i)(4-i), we can use the distributive property.
Step 1: Multiply the real terms together: 3 * 4 = 12.
Step 2: Multiply the imaginary terms together: 2i * -i = -2i^2. Remember that i^2 is equal to -1, so this becomes -2(-1) = 2.
Step 3: Multiply the real term with the imaginary term: 3 * -i = -3i.
Step 4: Combine the real terms and the imaginary terms: 12 + 2 - 3i.
Step 5: Simplify the expression: 14 - 3i.
Therefore, the simplified expression is 14 - 3i.