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

Question

Question

Answer 1

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.