The number of solutions of the equation `z^2+z=0` where z is a a complex number, is

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To find the number of solutions to the equation \( z^2 + z = 0 \) where \( z \) is a complex number, we can follow these steps:

### Step 1: Factor the equation
The given equation is:
\[ z^2 + z = 0 \]
We can factor out \( z \):
\[ z(z + 1) = 0 \]

### Step 2: Set each factor to zero
Now, we set each factor equal to zero:
1. \( z = 0 \)
2. \( z + 1 = 0 \)

### Step 3: Solve for \( z \)
From the first factor:
\[ z = 0 \]
From the second factor:
\[ z + 1 = 0 \implies z = -1 \]

### Step 4: Count the solutions
We have found two solutions:
1. \( z = 0 \)
2. \( z = -1 \)

Thus, the total number of solutions to the equation \( z^2 + z = 0 \) is **2**.

### Final Answer:
The number of solutions of the equation \( z^2 + z = 0 \) is **2**.

---