Question

find least positive integer n for which [(1+i√3)/1-i√3)]^n=1

Answer 1

$<b>answer is 9$

hope it helps

Answer 2

Hey there

Here ur answer

→ [ ( 1 + i √3 ) / ( 1 - i √3 ) ]^и  = 1

→ 1 + i √3 / 1 - i √3

→ ( 1 + i √3 ) ( 1 + i √3) / ( 1 - i √3 ) (1 + i √3)

→ ( 1 + I √3 )² / ( 1² - i² √3² )

→→ 1 - 3 + 2 i √3 / 1 + 3

→→  -1 + i √3 / 2

→→ -1 / 2 + i √3 / 2

→→ Sin ( -π / 6 ) + i cos ( -π / 6 )

thn,

[ 1 + i √3 / 1 - i √3 ]^n    =  [ Sin ( -π / 6 ) + i cos ( -π / 6 ) ]^n

                                     = Sin ( -  n π / 6 ) + i cos ( -  n π / 6 )

so,

Sin ( - n π / 6 ) + i cos ( - n π / 6 ) which becomes 1.

so,

n = 9.

∴ n = 9.

Hope this helps u

Be brainly