Question

If (1+i/1-i)x =1 then what is the value of x​

Answer 1

Answer: -i

Step-by-step explanation:

(1+i/1-i)x=1

{(1+i)/(1-i)×(1+i)/(1+i)} x=1

{(1+i)2/(1-i2)}x=1

(1+2i+i2/(1+1))x=1

(1+2i-1/(2))x=1

2ix=2

x=1/i

x=-i

Answer 2

$Given \: \: Question \: \: Is \: \\ \\ ( \frac{(1 + i)}{(1 - i)} ) {}^{x} = 1 \: \: \: find \: \: \: x \\ \\ Answer \: \\ \\ ( \frac{(1 + i) \times (1 + i)}{(1 - i) \times (1 + i)} ) {}^{x} = 1 \\ \\ (\frac{(1 + i) {}^{2} }{(1 {}^{2} - i {}^{2}) } ) {}^{x} = 1 \\ \\ (\frac{(1 + i {}^{2} + 2i )}{(1 + 1)} ) {}^{x} = 1 \\ \\ (\frac{(1 -1 + 2i)}{2} ) {}^{x} = 1 \\ \\ ( \frac{2i}{2} ) {}^{x} = 1 \\ \\ i {}^{x} = 1 \\ \\ now \: the \: question \: is \: what \: would \: be \: the \: \\ value \: of \: x \: so \: that \: \: i {}^{x} = 1 \\ \\ x \: \: must \: \: be \: \: \: 4n \:where \: n \: \: belongs \: \: to \: \: set \: \: of \: \: real \: \: numbers\\</p><p>so\:x=4n</p><p>$