Wednesday

March 4, 2015

March 4, 2015

Posted by **Mathslover** on Wednesday, May 29, 2013 at 11:54pm.

z1=r1(cosθ1+isinθ1)

z2=r2(cosθ2+isinθ2)

z3=r3(cosθ3+isinθ3)

z4=r4(cosθ4+isinθ4),

where ri is a real number and 0∘≤θi<360∘. What is the value of θ1+θ2+θ3+θ4 (in degrees)?

Details and assumptions

i is the imaginary unit satisfying i2=−1.

- Complex angles -
**Steve**, Thursday, May 30, 2013 at 10:54amIf the smallest angle is θ1, then the other angles are

θ1+90,θ1+180,θ1+270, so

θ1+θ2+θ3+θ4 = 4θ1 + 540

So, what is θ1?

Well, √i = (1+i)/√2, so

4−43√i = 4 - (43+43i)/√2 = 40.27 cis 229.027

So, the 4th root with smallest angle is

2.52 cis 57.26

So, θ1+θ2+θ3+θ4 = 4(57.26) + 540 = 769

**Answer this Question**

**Related Questions**

Trigonometry - There are four complex fourth roots to the number 4−4√...

Math - Calculus - The identity below is significant because it relates 3 ...

Trigonometry - Which of the following is equivalent to 1 − cos 2 θ/...

trigonometry - if cosθ=2/3 and tanθ<0 find the exact value sin(&#...

math - if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5&#...

trig - An object Is propelled upward at an angle θ, 45° < θ<90...

Calculus AP - hi again im really need help TextBook: James Stewart:Essential ...

Pre-Calculus - If θ represents an angle such that sin2θ = tanθ - ...

Trig - Given that csc θ = -4 and tan θ > 0, find the exact value of...

Trig - Given that tan θ = - (√3/8) and θ is in QII, find the ...