Question

Write each expression in the standard form for a complex number, a + bi.
A. [3(cos(27°)) + isin(27°)]^5
B. [2(cos(40°)) + isin(40°)]^6
For A i got 2.67+1.36i and for B i got 1.53+1.29i

Answer 1

(De Moivre's Theorem) Let z = r(cosθ + i sinθ)^n, and let n be a positive integer. Then zn = rn(cos nθ + i sin nθ) 1 Page 2 (i.e. in taking the nth power of z, we raise the modulus to its nth power and multiply the argument by n.)

So I will do one.
A. [3(cos(27°)) + isin(27°)]^5
[15(cos(5*27°)) + i5*sin(5*27°)] =
10.6+i 3.54

check that.

Answer 2

z^n = r^n cis(nθ)

Answer 3

Express in the form a + bi, where a and b are real numbers.
12(cos 5𝜋/4+ i sin 5𝜋/4)