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I need Trignometry help ASAP PLEASE

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.

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2 Answers

l r(sinθ + isinθ) l = l rcosθ + irsinθ l
 
                          = √[(rcosθ)2 + (rsinθ)2] = √[r2(cos2θ + sinθ)] = √(r2) = r
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