(1+i)^6+(1-i)^3 - Vidyadip

Question

$(1+\text{i})^6+(1-\text{i})^3$

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Answer

$(1+\text{i})^6+(1-\text{i})^3=\Big[(1+\text{i})^2\Big]^3+(1-\text{i})^3$
$=\big(1+\text{i}^2+2\text{i}\big)^3+\big(1-3\text{i}+3\text{i}^2-\text{i}^3\big)$
$=\big(1-1+2\text{i}\big)^3+\big(1-3\text{i}-3+\text{i}\big)$
$=8\text{i}^3-2-2\text{i}$
$=-2-10\text{i}$

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