Statement-1 : The locus of complex number z, satisfying `(z-2)^(n) =z^(n)` is a straight line .
and
Statement -2 : The equation of the form ax + by+c =0 in x -y plane is the general equation of striaght line.

Options

A. Statement -1 is True, Statement -2 is True, Statement -2 is a correct explanation for statement -9
B. Statement -1 is True, Statement -2 is True , Statement -2 is NOT a correct explanation for Statement -9
C. Statement -1 is True, Statement -2 is False
D. Statement -1 is Flase, Statement -2 is True

Answer

To solve the given problem, we need to analyze both statements regarding complex numbers and straight lines.

### Step 1: Analyze Statement 1
The first statement is:
\[ (z - 2)^n = z^n \]

### Step 2: Rewrite the Equation
We can rewrite this equation as:
\[ \frac{(z - 2)^n}{z^n} = 1 \]

### Step 3: Take Modulus of Both Sides
Taking the modulus of both sides gives us:
\[ \left| \frac{(z - 2)^n}{z^n} \right| = |1| \]
Since the modulus of 1 is 1, we have:
\[ \left| (z - 2)^n \right| = |z^n| \]

### Step 4: Simplify the Modulus
Using the property of moduli, we can simplify this to:
\[ |z - 2|^n = |z|^n \]

### Step 5: Cancel the Exponent
Since \(n\) is a positive integer, we can cancel \(n\) from both sides:
\[ |z - 2| = |z| \]

### Step 6: Interpret the Result
The equation \( |z - 2| = |z| \) means that the distance from the point \(z\) to the point \(2\) (on the real axis) is equal to the distance from \(z\) to the origin (0). This describes a perpendicular bisector of the line segment joining the points \(0\) and \(2\) in the complex plane.

### Step 7: Identify the Locus
The locus of points \(z\) satisfying this condition is indeed a straight line, specifically the vertical line \(x = 1\) in the Argand plane.

### Conclusion for Statement 1
Thus, Statement 1 is **true**.

### Step 8: Analyze Statement 2
The second statement is:
"The equation of the form \(ax + by + c = 0\) in the \(xy\) plane is the general equation of a straight line."

This is a well-known fact in coordinate geometry.

### Conclusion for Statement 2
Thus, Statement 2 is also **true**.

### Final Conclusion
Since both statements are true, we conclude that Statement 1 is true, and Statement 2 provides a correct explanation for Statement 1.