Express the given complex number in the form ^@ a + ib: ^@^@ (1 | Math Question and Answer | Edugain China

Login/Register Edugain for School

China

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

Answer:

$-4$

Step by Step Explanation:

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

You can reuse this answer
Creative Commons License