\[(3\imath +4)\imath \]
1
Regroup terms.
(4+3ı)ı(4+3\imath )\imath

2
Expand by distributing terms.
ı×4+ı×3ı\imath \times 4+\imath \times 3\imath

3
Regroup terms.
4ı+ı×3ı4\imath +\imath \times 3\imath

4
Use Product Rule: xaxb=xa+b{x}^{a}{x}^{b}={x}^{a+b}.
4ı+ı2×34\imath +{\imath }^{2}\times 3

5
Use Square Rule: i2=−1{i}^{2}=-1.
4ı−1×34\imath -1\times 3

6
Simplify  1×31\times 3  to  33.
4ı−34\imath -3

7
Regroup terms.
−3+4ı-3+4\imath

Done
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