Question

Solve for the real values of x and y in the equation yi(2x +)= (1- i)^3

Answer 1

x = - 0.5

y = 2

Explanation:

As per the given question,

We have

yi(2x + i)= (1- i)³

Expand it by using cubic identity

Cubic Identity:

(x-y)³ = x³ + 3xy² - 3x²y -y³

Therefore, we get

yi(2x + i)= (1³ + 3i² - 3i -i³)

2xy i + y i² = 1 -3 - 3i + i

(As i² = -1)

2xy i - y = -2i - 2

On comparing the real and imaginary parts on both side, we get

2xy = -2

And

y = 2

Therefore,

x = - 0.5

Hence, the required value of x = -0.5 and y = 2.