Let z = x+5 - 8-2x i where x is a real numberc Find the value of x such that z is a real number

To find the value of x such that z is a real number, we need to find the imaginary part of z, which is the coefficient of i, and set it equal to zero.

The imaginary part of z is given by (x+5) - (8-2x)i.

Setting this equal to zero, we have (x+5) - (8-2x)i = 0.

Expanding this equation, we get x + 5 - 8 + 2x = 0.

Combining like terms, we have 3x - 3 = 0.

Adding 3 to both sides of the equation, we get 3x = 3.

Dividing both sides by 3, we find x = 1.

Therefore, the value of x such that z is a real number is x = 1