write each complex number in trigometric form 1 6 6j 2 5 3

write each complex number in trigometric form

1. -6 - 6j

2. 5 - 3j

Write each complex number in rectangular form. Use simplest radical form where possible.

3. 6(cos 150 degrees + jsin 150 degrees)

4. 3 radical2(cos 135 degrees + jsin 135 degrees)

5. 4 / 65 degrees

Solution

1. -6-6j

TO write it in trigonometric form,we need r and theta

r=sqrt(-6)²+(-6)²= sqrt(72)=6 sqrt 2

tan theta= (-6)/-6=1

Tan theta=1

-6-6j= 6 sqrt2(cos (pi/4)+ j sin (pi/4))

2. 5-3j

r=sqrt(5²+(-3)²)

r=sqrt (25+9)=sqrt 34

tan theta= -3/5

theta =-pi/6

theta=5pi/6 approximately

5-3j=sqrt 34(cos (5pi/6) + j sin(5pi/6))

3. 6(cos 150 degrees + j sin 150 degrees)

rectagular form is z=a + bj

Where a= r cos theta

And b = r sin theta

here a=6 and theta=150

Therefore a= 6 cos 150 and b=6 sin 150

              a=5.2 approx and b=3

Therefore rectangular form

z= -5.2+ 3j

Theta=pi/4