Write -1 - i in exponential form.?

Answer 1

To convert ot polar (or exponential form) use the relations:

z = x + iy = R*e^(i*t)
R = sqrt(x^2 + y^2)
t = arctan(y/x)

Make sure you get the arctan in the correct quadrant.

In your case: x = -1, y = -1

So:

R = sqrt((-1)^2 + (-1)^2) = sqrt(2)
t = atan(-1/-1) = 5*pi/4

Finally: -1 - i = sqrt(2) * e^(i*5*pi/4)

Answer 2

-1 x 10 ^0

Answer 3

-1-i= e^ln(--1-i)
so let`s find ln(-1-i)
You should know that in complex a number has infinite logs
We´ll thake the" Principal Determination)
ln(-1-i) = ln(sqrt 2)+i*5pi/4
so -1-i= sqrt2*e^(i*5pi/4)

Answer 4

sqrt(2)exp(i(4k-3)pi/4)

For k=0, sqrt(2)exp(-3ipi/4)
or the positive sqrt(2)exp(5ipi/4)