If(1+1-1,thenfindthele least integral value of mm1-i)

1.	If(1+1-1,thenfindthele least integral value of mm1-i)
Answer» (1 + i)/(1 - i)}^m = 1 multiply (1 + i) numberator as well as denominator . {(1 + i)(1 + i)/(1 - i)(1 + i)}^m = 1 {(1 + i)²/(1² - (i)²)}^m = 1 {(1 + i² +2i)/2 }^m = 1 {( 2i)/2}^m = 1 {i}^m = 1 we know, i^4n = 1 where , n is an integer. so, m = 4n where n is an integerse.g m = 4 { because least positive integer 1 } hence, m = 4 ( answer )

Answer»

(1 + i)/(1 - i)}^m = 1

multiply (1 + i) numberator as well as denominator .

{(1 + i)(1 + i)/(1 - i)(1 + i)}^m = 1

{(1 + i)²/(1² - (i)²)}^m = 1

{(1 + i² +2i)/2 }^m = 1

{( 2i)/2}^m = 1

{i}^m = 1

we know, i^4n = 1 where , n is an integer.

so, m = 4n where n is an integerse.g m = 4 { because least positive integer 1 } hence, m = 4 ( answer )

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