a - b + 3i(sqrt(5)) = sqrt(5) + (a + b)i

Question

a - b + 3i(sqrt(5)) = sqrt(5) + (a + b)i

What is the value of (a^2) - (b^2)? (i = sqrt(-1))

Answer 1

(a - b) + (3√5)i = (√5) + (a+b)i

Two complex numbers are equal if and only if the real parts are equal and the imaginary parts are equal.

Assuming that a and b are real numbers, we then have:

a - b = √5

a + b = 3√5

So, a² - b² = (a - b)(a + b) = (√5)(3√5) = 15

Answer 2

a - b = √5

a + b = √5

a² - b² = 5