Absolute Value of Complex Number

The modulus or absolute value of the complex number -8i is:

The modulus or absolute value of the complex number -5+12i is: Hint: The modulus of a+bi is \left|a+bi\right|=\sqrt[]{\left(a\right)^2+\left(b\right)^2} where a is the real number part of the complex number and b is the "coefficient" of the imaginary part of the complex number. The modulus represents the DISTANCE FROM THE ORIGIN \left(0+0i\right) TO THE GIVEN COMPLEX NUMBER, so the modulus is a positive real number for any nonzero complex number. You can use the given formula or you can construct a right triangle using the origin, the given complex number's point, and a perpendicular through the given complex number's point and the horizontal x-axis. Then apply the Pythagorean Theorem such that the modulus represents the HYPOTENUSE of the constructed right triangle.

Find the absolute value of each complex number. |3 - 9i|

• 3\(\sqrt{10}\)

• \( \sqrt{97} \)

• \( \sqrt{13} \)

• 4i\(\sqrt{3}\)

Find the absolute value of each complex number. |-2 + 4i|

• \( \sqrt{13} \)

• 2

• \( 2\sqrt{5} \)

• \( \sqrt{10} \)

Find the absolute value of each complex number. |5 + 5i|

• \( \sqrt{41} \)

• 3

• \( \sqrt{61} \)

• 5\(\sqrt{2}\)

Find the absolute value of each complex number. |4 - 4i|

• \( \sqrt{34} \)

• 4\(\sqrt{2}\)

• 4

• \( 2\sqrt{2} \)

Let w=-√3/2 + 1/2 i calculate the modulus and argument.

• 3, 120^o

• 5, 270^o

• 1, 150^o

• Not Possible