Modulus of complex number 3i-4 is:

Options

A. `-1`
B. 25
C. 5
D. `-7`

Answer

To find the modulus of the complex number \(3i - 4\), we will follow these steps:

### Step 1: Identify the real and imaginary parts
The complex number \(3i - 4\) can be rewritten in the standard form \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part. Here, we can express it as:
\[ -4 + 3i \]
Thus, we have:
- Real part \(a = -4\)
- Imaginary part \(b = 3\)

### Step 2: Use the modulus formula
The modulus of a complex number \(z = a + bi\) is given by the formula:
\[ |z| = \sqrt{a^2 + b^2} \]

### Step 3: Substitute the values into the formula
Now, substituting the values of \(a\) and \(b\) into the modulus formula:
\[ |z| = \sqrt{(-4)^2 + (3)^2} \]

### Step 4: Calculate the squares
Calculating the squares:
\[ |z| = \sqrt{16 + 9} \]

### Step 5: Add the results
Now, add the results:
\[ |z| = \sqrt{25} \]

### Step 6: Take the square root
Finally, take the square root:
\[ |z| = 5 \]

Thus, the modulus of the complex number \(3i - 4\) is \(5\).

### Final Answer:
The modulus of the complex number \(3i - 4\) is \(5\).

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