I need Trignometry help ASAP PLEASE

Question

I need help with these trigonometry problems. I would really appreciate it if you could help me. Here is the problem: Problem #3 – Show that |r(cosθ + isinθ )| = r. Second Question: – Find the complex roots of z^4 + 256 = 0 and use them to factor the expression into irreducible quadratics with real coefficients.

Answer 1

l r(sinθ + isinθ) l = l rcosθ + irsinθ l

 

                          = √[(rcosθ)² + (rsinθ)²] = √[r²(cos²θ + sin² θ)] = √(r²) = r

Answer 2

cosθ = sinθ

 

and the two angles are complementary to each other.

 

 

 

 

We can rewrite (z⁴ + 256) as    (z⁴ - 256i²).

 

Factoring this difference of perfect squares,

 

(z² - 16i)(z² + 16i) = 0