Question

How to write (√2 +i√2)³ in trigonometric form?

Answer 1

first change the complex number to trig form

Answer 2

how do I do that

Answer 3

it helps to graph the complex number on a modified x y coordinate plane. the y axis becomes the ' i ' axis

Answer 4

the x axis stands for real number numbers

Answer 5

it's the square root that's confusing me

Answer 6

If we are given the complex number
$$ \Large a + ib \\
\Large \text{this is equal to}\\
\Large r(cos(\theta) + i sin(\theta))\\
\Large \text {where}~~ r =\sqrt{a^2+b^2} ~,~ \theta =\arctan (b/a)

$$

Answer 7

i got r=2 and theta= 45 or pi/4 so 2(cos(pi/4)+isin(pi/4))?

Answer 8

so does that mean it's 8(cos(3pi/4)+isin(3pi/4))?

Answer 9

@perl

Answer 10

$$
\large (\sqrt{2}+i\sqrt{2})^3 \\
\large =( 2 \cos (\pi/4) + i \sin(\pi/4))^3
\large= 2^3 (cos(\pi/4 * 3 ) +i \sin(\pi/4*3))
$$

Answer 11

by demoivre's theorem

Answer 12

oh, okay. Thank you!