NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

Question : 36

Total: 52

If x - iy = √

a−ib

c−id

, prove that (x2+y2)2 =

a2+b2

c2+d2

Solution:

We have given, x - iy = √

a−ib

c−id

... (i)
Squaring (i) both sides, we get
(x−iy)2 =

a−ib

c−id

⇒ |(x−iy)2| = |

a−ib

c−id

|
⇒ |x−iy|2 =

|a−ib|

|c−id|

⇒ (√x2+y2)2 =

√a2+b2

√c2+d2

⇒ x2+y2 =

√a2+b2

√c2+d2

... (ii)
Squaring (ii) sides, we get
(x2+y2)2 =

a2+b2

c2+d2

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