Complex Numbers Question 1

$$ (2+3i)-(5-i)$$

In the complex number system, which of the following is equivalent to the expression above? (Note: $ i=\sqrt{-1}$)

$ 0 $

$ 3-4i $

$ -3+4i $

$ -3-2i $

Approach

Similar to polynomials, we combine like terms. Make sure to distribute the negative sign first.

$$ (2+3i)-(5-i) $$ $$ 2+3i-5+i $$ $$ \underbrace{2-5}_\text{real component}+\underbrace{3i+i}_\text{imaginary component} $$ $$ = -3+4i $$