Question - Multiplication of Complex Numbers
Solution:
The image shows the multiplication of two complex numbers: $$ (2 - i) $$ and $$ (1 + i) $$, where $$ i $$ is the imaginary unit with the property that $$ i^2 = -1 $$.To solve this, we apply the distributive property (FOIL method) as we would with binomials:$$(2 - i)(1 + i) = 2(1) + 2(i) - i(1) - i(i)$$Now we simplify each term:$$= 2 + 2i - i - i^2$$Remember that $$ i^2 = -1 $$, so the expression becomes:$$= 2 + 2i - i + 1$$Combine like terms:$$= (2 + 1) + (2i - i)$$$$= 3 + i$$So, the product of $$ (2 - i) $$ and $$ (1 + i) $$ is $$ 3 + i $$.
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