Find the modulus and the argument for the complex number. $z = - i$
A) $r = - 1 , \theta = \pi / 2$

B) $r = 1 , \theta = \pi$

C) $r= i , \theta = 0$

D) $r= \sqrt { 2 } , \theta = 3 \pi / 2$

E) $r = 1 , \theta = 3 \pi / 2$

Question

Find the modulus and the argument for the complex number. $z = - i$
A) $r = - 1 , \theta = \pi / 2$

B) $r = 1 , \theta = \pi$

C) $r= i , \theta = 0$

D) $r= \sqrt { 2 } , \theta = 3 \pi / 2$

E) $r = 1 , \theta = 3 \pi / 2$

Quizplus · Accepted Answer

The modulus of a complex number is the distance from the origin to the point representing the number in the complex plane. In this case, the modulus of $-i$ is 1, because it is 1 unit away from the origin on the imaginary axis.

The argument of a complex number is the angle between the positive real axis and the line connecting the origin to the point representing the number in the complex plane. In this case, the argument is $3\pi/2$, because the point representing $-i$ is 270 degrees counterclockwise from the positive real axis (or equivalently, 90 degrees clockwise from the positive imaginary axis).

Therefore, the correct answer is E, with modulus 1 and argument $3\pi/2$.

Find the Modulus and the Argument for the Complex Number z=−iz = - iz=−i

Find the Modulus and the Argument for the Complex Number $z = - i$