Question

Question #e8f6b

Answer 1

`6.4` (nearest tenth)

Explanation:

the two parts of the complex number are graphed on different axes.

`5` is the real part of the number, while `-4i` is the imaginary part.

`5` is graphed as `5` to the right, on the real axis.

`-4i` is graphed as `4` down, on the imaginary axis.

the modulus is the point's distance from `0`. (in the picture, the distance is shown by a thin grey line)

the value of the modulus (i.e. the length of the line) can be calculated using Pythagoras' theorem, where the modulus is the hypotenuse.

`a^2 + b^2 = c^2`

`a` and `b` are the distances from the real and imaginary axes. here, these are `5` and `4`.

`5^2 + 4^2 = c^2`

`c^2 = 25 + 16 = 41`

`c = sqrt41`

this means that the length of the line, and therefore the value of the modulus, is `sqrt41` as an exact value.

rounded, it is `6.4` to the nearest tenth.