Which complex number's graph is shown?

Option D.

Step-by-step explanation:

When we want to graph a complex number in a coordinate axis, the real part of the complex number is represented by the x-axis, and the complex part is represented by the y-axis.

in this case, we can see that the coordinates of the point are:

(-2, 2)

Then the complex number is:

Z = -2 + 2*i

Now we need to see which one of the given options is equal to this.

Let's check the real part for every option, so we can discard some of them:

A) real part = -2*cos(135°) = 1.41  (we can discard this option)

B) real part = 2*cos(7*pi/4) = 1.41 (we can discard this option)

C) real part = √2*2*cos(225°) = -2

D) real part = √2*2*cos(3*pi/4) = -2  

So options C or D are the correct one, now let's check the complex part for each one

C) complex part = √2*2*sin(225°) = -2    (we can discard this option)

D) complex part =  √2*2*sin(3*pi/4) = 2

So the correct one is the D option.

14

step-by-step explanation:

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %