Let z 2

Let z = 2 - sqrt(3i). Find z6 and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3

Correct answer:

x =  8.999
y =  2.2439

Step-by-step explanation:

3i = x1 + y1   i x1=3/21.2247 y1=x1=1.22471.2247  z = x2 + i y2 x2=2x1=21.22470.7753 y2=0y1=01.22471.2247  r=z r=x22+y22=0.77532+(1.2247)21.4495 θ=arctan(y2/x2)=arctan((1.2247)/0.7753)1.0065 rad  z6=r6 (cos 6θ + i sin 6θ)  r2=r6=1.449569.2745 θ2=6 θ=6 (1.0065)6.0388 rad  x=r2 cos(θ2)=9.2745 cos((6.0388))=8.999
y=r2 sin(θ2)=9.2745 sin((6.0388))=2.2439

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Try our complex numbers calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: