`-6 + 8i` Plot the complex number and find its absolute value.

Expert Answers
sciencesolve eNotes educator| Certified Educator

The absolute value of a complex number `z = a + b*i` is `|z| = sqrt(a^2 + b^2)` . According to this formula, you need to determine a and b, such that:

`a = -6, b = 8`

`|z| = sqrt((-6)^2 + 8^2)`

`|z| = sqrt(36 + 64)`

`|z| = sqrt 100`

`|z| = 10`

Hence, the distance of the complex number `z = -6 + 8i` from the origin is given by its absolute value `|z| = 10` .

In the Argand diagram, the complex number` z = -6 + 8i` is the point `(-6,8)` or the vector from the origin to the point `(-6,8)` .

sciencesolve eNotes educator| Certified Educator

The absolute value of a complex number z = a + b*i is |z| = sqrt(a^2 + b^2). According to this formula, you need to determine a and b, such that:

a = -6, b = 8

|z| = sqrt((-6)^2 + 8^2)

|z| = sqrt(36 + 64)

|z| = sqrt 100

|z| = 10

Hence, the distance of the complex number z = -6 + 8i from the origin is given by its absolute value |z| = 10.

In the Argand diagram, the complex number z = -6 + 8i is the point (-6,8) or the vector from the origin to the point (-6,8).

loves2learn | Student

See the attached image for the plot

 

The absolute value is equal to `sqrt(a^2+b^2)`

`=sqrt(-6^2+8^2)`

`=10`