Posted by tabby on Friday, April 13, 2012 at 3:44pm.
Teach me how to express 5sqrt3 - 5i in polar form please.
I don't want you to do the work for me. Just show me the steps I need to do the work properly on my own. Otherwise I will not pass this class or the exam when I enter college, and I do not want to retake PreCalc.
Its a multiple choice homework question with answer choices:
a: 10(cos 11pi/6 + i sin 11pi/6)
b: 10(cos 11pi/6 - i sin 11pi/6)
c: 5 (cos 11pi/6 + i sin 11pi/6)
d: 10(cos 5pi/3 + i sin 5pi/3)
I did as much work as I could guess at, and came up with r=10sqrt2,
arctan=1/sqrt3 which equals sqrt3/3.I know that sqrt3/3 = tan 30 and 210 degrees. But now I am stuck.
Where do I go from here - or is this even the right way to try to solve this equation? Please help me.
- Trig/PreCalc - Reiny, Friday, April 13, 2012 at 8:49pm
start by graphing 5√3 - 5i
as (5√3, -5) in the argand plane
which would be in quadrant IV
r^2 = (5√3)^2 + (-5)^2 = 100
r = 10
we also know that tanŲ = -5/(5√3) = -1/√3
( I know that tan 30° = tan π/6 = 1/√3)
but my angle is in IV, so Ų = 11π/6 or 330°
so 5√3 - 5i = 10(cos 11π/6 + i sin 11π/6)
RS = 10( √3/2 + i(-1/2)
= 5√3 - 5i
= original complex number
so in summary
for a + bi
1. sketch (a,b) to see which quadrant you are in
2. evaluate r,
with r^2 = a^2 + b^2 ---> r = | √(a^2 + b^2)
3. from tan Ų = |b/a| find the acute angel Ų
- for I, Ų is that acute angle
- for II , Ų = π - acute angle
- for III , Ų = π + acute angle
- for IV, Ų = 2π - acute angle
a + bi = r( cosŲ + isinŲ)
use your calculator to verfiy your answer.
Answer This Question
More Related Questions
- Trig?Precalc - write the rectangular equation x^2+y^2=6 in polar form. I do not ...
- Math - Can somebody please explain to me how to factor trinomials that contain ...
- trig - 6. Compute the modulus and argument of each complex number. I did a-c and...
- Math - I already figured most of these out, but I need to learn how to SHOW MY ...
- Nedd Help Please - PreCalc - The coordinates of the five quarter points for y=...
- Calculus - Use the function f to solve the following: a) Local minima, local ...
- physics - A resistor (R = 900 ), a capacitor (C = 0.25 µF), and an inductor (L...
- Help Needed for PreCalc - List all points on the graph of y=tanx on the interval...
- Trigonometry - rectangular form to polar form xy=12 rsinĘ rcosĘ=12 would the ...
- Math - Please help me with this step by step show your work problem. |-4b-8|+|-1...