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4-1.Complex numbers
medium
જો ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^m} = 1,$તો $m$ ની . . . ન્યૂનતમ ધન પુર્ણાક માટે
A
$2$
B
$4$
C
$8$
D
એકપણ નહીં.
(IIT-1982)
Solution
(b)$\frac{{1 + i}}{{1 – i}} = \frac{{1 + i}}{{1 – i}} \times \frac{{1 + i}}{{1 + i}} = \frac{{{{(1 + i)}^2}}}{2} = \frac{{2i}}{2} = i$
$\therefore $${\left( {\frac{{1 + i}}{{1 – i}}} \right)^m} = {i^m} = 1$(as given)
So the least value of $m = 4$.
$\{ \because {i^4} = 1\} $
Standard 11
Mathematics