Question

simplify (2 - 3i)(1 + 5i) - 3(-2 + i). 23 + 4i

Explanation:

Step1: Multiply the complex numbers

First, multiply \((2 - 3i)(1 + 5i)\) using the distributive property (FOIL method):

$$
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Since \(i^2=- 1\), we have:

$$
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Step2: Simplify the second term

Simplify \(-3(-2 + i)\):

$$ -3(-2 + i)=(-3)\times(-2)+(-3)\times i = 6-3i $$

Step3: Subtract the two results

Now, subtract the second result from the first: \((17 + 7i)-(6 - 3i)\)

$$
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Wait, there is a mistake in the previous calculation. Let's re - do the multiplication of \((2-3i)(1 + 5i)\) correctly:

$$
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Then \(-3(-2 + i)=6-3i\)

Now, \((17 + 7i)+(6 - 3i)\) (because the original expression is \((2 - 3i)(1 + 5i)-3(-2 + i)\), which is \((17 + 7i)-(-6 + 3i)\)? Wait, no, the original expression is \((2 - 3i)(1 + 5i)-3(-2 + i)\), so it is \((17 + 7i)-3(-2 + i)=(17 + 7i)+6 - 3i\)

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Answer:

\(23+4i\)