Solve this

Question:

Express $(2-3 i)^{3}$ in the form $(a+i b)$

 

Solution:

We have, $(2-3 i)^{3}$

$=2^{3}-3 \times 2^{2} \times 3 i-3 \times 2 \times(3 i)^{2}-(3 i)^{3}$

$=8-36 i+54+27 i$

$=46-9 i .$

 

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