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RD Chapter 13 Complex Numbers Ex 13.2 Solutions

Question - 11 : -

If [(1+i)/(1-i)]3 – [(1-i)/(1+i)]3 = x+ iy, find (x, y)

Answer - 11 : -

Given:

[(1+i)/(1-i)]3 –[(1-i)/(1+i)]3 = x + iy

Let us rationalize thedenominator, we get

i3–(-i)=x + iy

2i=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

 The values of xand y are 0 and -2.

Question - 12 : -

If (1+i)2 / (2-i) = x + iy, find x + y

Answer - 12 : -

Given:

(1+i)2 /(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

 The value of (x+ y) is 2/5

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