Question

Calculate |4+7i| the absolute value of 4+7i is equal to the square root of ____.

A) 16

B) 49

C) 65

D) 8

Answer 1

The absolute value of the complex number 4+7i is the square root of 65.

Step-by-step explanation:

To calculate the absolute value (or magnitude) of the complex number 4+7i, we use the formula for the modulus of a complex number, which is √(a² + b²), where 'a' is the real part and 'b' is the imaginary part.

For the complex number 4+7i:

• a = 4
• b = 7

Substitute these values into the formula:

√(a² + b²) = √(4² + 7²) = √(16 + 49) = √65

Therefore, the absolute value of 4+7i is the square root of 65.