If 2x2 + (x2 - y)i = (8 - 3i), find the values of x and y

  1. x = -1, 1 and y = 4
  2. x = 0, y = 3
  3. x = -2, 2 and y = 7
  4. x = 2, 3 and y = 7, 12 

Answer (Detailed Solution Below)

Option 3 : x = -2, 2 and y = 7
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Detailed Solution

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Concept:

Equality of complex numbers:

Two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 are equal if and only if x1 = x2 and y1 = y2

Or Re (z1) = Re (z2) and Im (z1) = Im (z2)

 

Calculation:

Given that, 2x2 + (x2 - y)i = (8 - 3i)

Comparing the real and imaginary parts,

⇒ 2x2 = 8 

⇒ x2 = 4

⇒ x = -2, 2

And, x2 - y = -3

⇒ 4 - y = -3               [∵ x2 = 4]

⇒ y = 7 

Hence, option (3) is correct.
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