Question

4(3 - 2i) + (2 + 3i)^2

Explanation:

Step1: Expand the terms

First, expand \(4(3 - 2i)\) and \((2 + 3i)^2\) using the distributive property (for the first term) and the formula \((a + b)^2 = a^2 + 2ab + b^2\) (for the second term).

For \(4(3 - 2i)\):

$$ 4(3 - 2i)=4\times3-4\times2i = 12 - 8i $$

For \((2 + 3i)^2\):
Let \(a = 2\) and \(b = 3i\). Then,

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Since \(i^2=- 1\), we substitute that in:

$$ 4 + 12i+9\times(-1)=4 + 12i-9=-5 + 12i $$

Step2: Add the two expanded expressions

Now, add \(12 - 8i\) and \(-5 + 12i\):

$$ (12 - 8i)+(-5 + 12i)=(12-5)+(-8i + 12i) $$

Simplify the real and imaginary parts separately:

$$ 7 + 4i $$

Answer:

\(7 + 4i\)