Math

use Demoivre's Theorem to find the indicated power of the complex number. Express the result in standard form.

(2+2i)^6

a=2 b=2 n=6

r=sqrt 2^2 + 2^2 = sqrt8
Q=7pi/4

(sqrt8)^6 = 512
512(cos 6/1 x 7pi/4) + i sin 6 x 7pi/4
512 (cos 21pi/2) + i sin (21pi/2)
512(cos pi/2) + i (sin pi/2)
512(2+2i)

1024 + 1024i

Is this correct?

1. 👍
2. 👎
3. 👁

Similar Questions

1. Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

2. Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x)=2-x^2 on the interval [0,√2). If so, find the x-coordinates of the point(s) guaranteed by the theorem a) No, the Mean Value Theorem for Integrals

3. MATH

please help me... 1. When squaring a complex number using De Moivre's theorem, there are two answers. TRUE FALSE i think it's true, but I'm not sure. thanks.

4. Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = √x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. a) No, the theorem does not apply b)

1. achimota secondary school

when a certain number is added to 11 and the result is multiplied by 3, the final result is 45. Find the number.

2. Calculus

How is the product of a complex number and a real number represented on the coordinate plane? A)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a counterclockwise

3. Math

According to the Pythagorean theorem, which of the following statements below is true for the triangle in the diagram? (1) a2+4 to 2 power= 5 2 power. 5 (2) a2-4 to2 power=5 2 power. A. (3) a2+5 to2 power=4 2 power (4) a2-5 to

4. Algebra 2

What is the product of a complex conjugated? The product of complex conjugates is a difference of two squares it is always a real number. The product a complex conjugates may be written in standard form as a + bi where neither a

1. physics

The disk shaped head of a pin is 1.0 mm in diameter. Which of the following is the best estimate of the number of atoms in the layer of atoms on the top of the surface of the pinhead? 1. 10 to the 34th power 2. 10 to the 19th
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.jiskha.com/questions/355538/use-demoivres-theorem-to-find-the-indicated-power-of-the-complex-number-express-the", "fetch_time": 1618185254000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2021-17/segments/1618038065903.7/warc/CC-MAIN-20210411233715-20210412023715-00130.warc.gz", "warc_record_offset": 959235102, "warc_record_length": 4784, "token_count": 734, "char_count": 2361, "score": 3.71875, "int_score": 4, "crawl": "CC-MAIN-2021-17", "snapshot_type": "latest", "language": "en", "language_score": 0.7893871068954468, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00048-of-00064.parquet"}