Simplify each of the following and express it in the form a + ib

Question:

Simplify each of the following and express it in the form a + ib

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

 

Solution:

Given: $(3+4 i)(2-3 i)$

Firstly, we open the brackets

$3 \times 2+3 \times(-3 i)+4 i \times 2-4 i \times 3 i$

$=6-9 i+8 i-12 i^{2}$

$=6-i-12(-1)\left[\because, i^{2}=-1\right]$

$=6-i+12$

$=18-i$

 

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