(2-4i)-(-4+i)=
2-4i +4-i= 6-4i
To simplify the expression (2-4i)-(-4+i), you can follow these steps:
1. Distribute the negative sign to each term inside the parentheses. This will change the sign of each term within the second set of parentheses.
(2-4i)-(-4+i) becomes 2 - 4i + 4 - i.
2. Combine like terms. Group the real numbers (2 and 4) together and also group the imaginary terms (-4i and -i) together.
(2 - 4i) + (4 - i) becomes (2 + 4) + (-4i - i).
3. Simplify each group separately. Addition is associative, so you can first simplify the real numbers: 2 + 4 = 6.
The expression now becomes 6 + (-4i - i).
4. Simplify the imaginary numbers: -4i - i. Subtraction is a special case for complex numbers, where you can treat the imaginary unit (i) as a separate variable.
-4i - i can be written as (-4 - 1)i = -5i.
5. Substitute the simplified values back into the expression: 6 + (-5i).
Therefore, (2-4i)-(-4+i) simplifies to 6 - 5i.