Can someone help me convert a number into TRIGONOMETIC FORM?

Question

the number is -729i. Please Help me covert this number into trigonemetric form!

Answer 1

"trigonometric form" is pretty much the same as polar coordinate form.

-729i is straight down the y-axis in the complex number plane, so the angle is 3/2pi.

the radius r is 729. It's the square root of the sum of the squares of the complex and non-complex parts. In this case the non-complex part is 0, so sqrt(0^2 + 729^2) = sqrt(729^2) = 729.

You'd write it as:
r(cos(t) + i*sin(t))
which is usually abbreviated as:
r*cis(t)

So your answer is:
729 ( cos(3pi/2) + i*sin(3pi/2) )
or
729 cis(3pi/2)

Answer 2

Well, if i = sqrt(-1), then

Euler's equation gives Ae^(ix) = Acos(x)+i Asin(x)

So A = 729. Now we need to find out how to represent -i.

Now, think about the unit circle, and what angle gives a value of -i? It is at 270 degrees or -90 degrees, or if you like radians, 3/2 pi.

So -729i = 729 e^(i 3/2 pi)

An equally correct answer would be -729^e(i pi/2)

Answer 3

Trig form would be r cis theta.

r=sqrt(a^2+b^2)
r=sqrt(0^2+(-729)^2)
r=729
theta = arctan(-729/0), but b/c 0 cannot be in the denominator of a fraction, imagine plotting the point (0,-729); it would be on the negative y-axis. That is 270 degrees or 3pi/2 radian.

Trig form: 729 cis 3pi/2

Answer 4

18/5 is eighteen divided by skill of 5 do this branch and you get 3 with a the remainder of 5, so the respond is 3 3/5. 3/5 is already in easiest words. 60/8 is 60 divided by skill of 8. that's 7 with a the remainder of four, so the respond is 7 4/8. 4/8 might nicely be decreased to a million/2, so the terrific answer is 7 a million/2. For that final one, you may cut back it first: 60/8 = 15/2. 15/2 is 7 with a the remainder of a million, so lower back it truly is 7 a million/2