Question

find the least positive integral value of m satisfying ([1+i]/[1-i])^m = 1 guys plsss help me

Answer 1

Answer:

4

Step-by-step explanation:

Hi ,

Given that [(1 + i)/(1 - i)]^m = 1

Consider (1 + i)/(1 - i)

Multiplying Numerator and denominator by ( 1 + i), we get

(1 + i)²/(1 + i)*(1 - i)

= (1 + i)²/(1 - i²)

= (1 + i² + 2i)/(1 + 1), since i² = -1

= 2i/2

= i

So given expression, when simplified is equal to

i^m = 1

But we know that for every power which is a multiple of 4 is 1

i^{4k} = 1 where k is any integer

The least positive value of k satisfying above equation is k = 1

Hence , least positive integral value of m = 4

Hope, it helps !