The Total solution for NCERT class 6-12
If [(1+i)/(1-i)]3┬атАУ [(1-i)/(1+i)]3┬а= x+ iy, find (x, y)
Answer - 11 : -
Given:
[(1+i)/(1-i)]3┬атАУ[(1-i)/(1+i)]3┬а= x + iy
Let us rationalize thedenominator, we get
i3тАУ(-i)3┬а=x + iy
2i3┬а=x + iy
2i2.i = x +iy
2(-1)I = x + iy
-2i = x + iy
Equating Real andImaginary parts on both sides we get
x = 0 and y = -2
тИ┤┬аThe values of xand y are 0 and -2.
If (1+i)2┬а/ (2-i) = x + iy, find x + y
Answer - 12 : -
(1+i)2┬а/(2-i) = x + iy
Upon expansion we get,
Let us equate real andimaginary parts on both sides we get,
x = -2/5 and y = 4/5
so,
x + y = -2/5 + 4/5
= (-2+4)/5
= 2/5
тИ┤┬аThe value of (x+ y) is 2/5