Express the given complex number in the form ^@ a + ib: ^@
^@ (1 - i )^{ 4 } ^@


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Answer:

^@ -4 ^@

Step by Step Explanation:
  1. ^@\begin{align} (1 - i)^{ 4 } &= \left\{ (1 - i)^2 \right\}^2 \\ &= \left\{ 1^2 + i^2 - 2i \right\}^2 \\ &= \left\{ 1 - 1 - 2i \right\}^2 && [\text{Since } i^2 = -1] \\ &= \left\{ - 2i \right\}^2 \\ &= 4 i^2 \\ &= -4 && [\text{Since } i^2 = -1] \end{align}^@
  2. Hence, the representation of ^@ (1 - i )^{ 4 } ^@ in the form ^@ a + ib ^@ is ^@ -4 ^@.

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