Question

Find the modulus and amplitude for each of the following complex number-4-4i

Answer 1

Answer:

Modulus =

$4 \sqrt{2}$

Amplitude =

225°

Step-by-step explanation:

The modulus of a complex number is found by adding the squares of the real part and the imaginary part's coefficients and taking their square root.

Here, it will be

$\sqrt{ {4}^{2} + {4}^{2} } \\ = \sqrt{32} \\ = 4 \sqrt{2}$

The amplitude of the complex number is the angle it forms with the x-axis on a graph

In this question, the slope of line on which the number lies is -4/-4 = 1

tan x = 1

x = 45° or 225°

Since both coefficients are negative, the point lies in the third quadrant.

So x = 225°

Answer 2

Answer:

Step-by-step explanation:

Let x=-4-4i

a=-4 and b=-4

Therefore, |z| modulus =√x^2+y^2

=√(-4)+(-4)

=√16+16

=√32

Modulus =√32

=√16×2

=4√2

Therefore, amplitude =tan^-1 b/a

=tan^-1 -4/-4

=tan^-1 1

=π\4

=45°