Question

(1+i)^4

express in a+ib form​

Answer 1

Step-by-step explanation:

${(1 + i)}^{2} {(1 + i)}^{2}$

$( {1}^{2} + 2(1)(i)+ {i}^{2} )({1}^{2} + 2(1)(i)+ {i}^{2})$

$(1 + 2i + {i}^{2} )(1 + 2i + {i}^{2})$

$1(1 + 2i + {i}^{2} ) + 2i(1 + 2i + {i}^{2} ) + {i}^{2} (1 + 2i + {i}^{2} )$

$1 + 2i + {i}^{2} + 2i + 4 {i}^{2} + 2 {i}^{3} + {i}^{2} + 2 {i}^{3} + {i}^{4}$

$1 + 2i + 2i + {i}^{2} + 4 {i}^{2} + {i}^{2} + 2 {i}^{3} + 2 {i}^{3} + {i}^{4}$

$1 + 4i + 6 {i}^{2} + 4 {i}^{3} + {i}^{4}$

1+i(4+6i+4i^2+I^3)

hope it's helpful