Question

Z= (1-i)^4
pls can u guys give me this answer pls ​

Answer 1

$\large\bf \implies \large\bf z = {(1 - i)}^{4}$

Where i = √-1

$\implies \sf z = {(1 - i)}^{2} {(1 - i)}^{2}$

We know that :-

$\underline{\boxed{ \large\bf{ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab}}}$

$\sf\implies z = ({1}^{2} + {i}^{2} - 2i) ({1}^{2} + {i}^{2} - 2i)$

$\sf\implies z = ({1} + {i}^{2} - 2i) ({1} + {i}^{2} - 2i)$

We know that :-

$\underline{\boxed{ \large\bf{ {i}^{2} = - 1}}}$

$\sf\implies z = ({1} - 1 - 2i) ({1} - 1 - 2i) \div$

$\sf\implies z = (0 - 2i) (0- 2i)$

$\sf\implies z = {(- 2i)}^{2}$

$\sf\implies z = 4 \times ( - 1)$

$\sf\implies z = - 4$

Answer : -4