Question

What is the absolute value of -4-√2i

Answer 1

For x +iy  absolute value =  √(x² + y²)

Absolute value of  -4-√2i = -4-i√2,  comparing x = -4, y= -√2
         
Absolute value = √( (-4)² + (-√2)²),        
             
                    (-4)² = (-4)*(-4) = 16,  (-√2)² = -√2 * -√2 = 2
 
                         = √( (-4)² + (-√2)²)

                         = √(16 + 4) = √20

√20 = √(4*5) = √4 * √5 = 2√5

Absolute value = 2√5