Question
Evaluate the expression (2-4i)(1-i) and write the result in the form a+bi
Answers
Answered by
GPT-4o mini
To evaluate the expression \((2 - 4i)(1 - i)\), we can use the distributive property (also known as the FOIL method for binomials).
1. **First**: \(2 \cdot 1 = 2\)
2. **Outer**: \(2 \cdot (-i) = -2i\)
3. **Inner**: \(-4i \cdot 1 = -4i\)
4. **Last**: \(-4i \cdot (-i) = 4i^2\)
Now, recall that \(i^2 = -1\). Thus, \(4i^2 = 4(-1) = -4\).
Now, we can combine all the parts:
\[
(2 - 4i)(1 - i) = 2 - 2i - 4i - 4
\]
Combine like terms:
\[
2 - 4 - 2i - 4i = -2 - 6i
\]
Thus, the expression \((2 - 4i)(1 - i)\) in the form \(a + bi\) is:
\[
\boxed{-2 - 6i}
\]
1. **First**: \(2 \cdot 1 = 2\)
2. **Outer**: \(2 \cdot (-i) = -2i\)
3. **Inner**: \(-4i \cdot 1 = -4i\)
4. **Last**: \(-4i \cdot (-i) = 4i^2\)
Now, recall that \(i^2 = -1\). Thus, \(4i^2 = 4(-1) = -4\).
Now, we can combine all the parts:
\[
(2 - 4i)(1 - i) = 2 - 2i - 4i - 4
\]
Combine like terms:
\[
2 - 4 - 2i - 4i = -2 - 6i
\]
Thus, the expression \((2 - 4i)(1 - i)\) in the form \(a + bi\) is:
\[
\boxed{-2 - 6i}
\]
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