Question

Write z1 and z2 in polar form, and then find z1(z2) and z1/z2. Rewrite the results in the form a+bi

Answer 1

z1= -5i z2=2+21

Answer 2

@zepdrix :)

Answer 3

for z1 polar I got = 5cis(3pi/2)
for z2 polar I got = 2(sq2)cis(5pi4)

Answer 4

Is that correct?

Answer 5

z2 is incorrect

Answer 6

z2 = 2 + 2i ?

Answer 7

yeah, hm

Answer 8

z2= 2(sq2)cis(pi4)

Answer 9

Doesn't it have to be where theta is positive? ie. Quadrant 3?

Answer 10

theta is positive in quadrant 1

Answer 11

im not sure how you got that angle, the complex number 2 + 2i is in quadrant 1 , in the complex plane

Answer 12

oh shoot. Yeah, i see now.

Answer 13

fail. haha thanks.

Answer 14

ok, three parts left :)

Answer 15

z1 times z2

Answer 16

let me try it out on paper.

Answer 17

z1(z2)= 10(sq2)cis(7pi/4)

Answer 18

\[\large \rm if ~ z_1 =r_1\angle \theta_1,~ z_2 =r_2\angle \theta_2 \\ \large z_1 \cdot z_2 = r_1\cdot r_2~ \angle \left ( \theta_1 + \theta_2 \right )\]

Answer 19

yes thats correct

Answer 20

what i'm working with is:
\[z _{1}z _{2}=r _{1}r _{2}(\cos(\theta _{1}+\theta _{2})+isin(\theta _{1}+\theta _{2}))\]

Answer 21

yay! next is z1/z2

Answer 22

divide radii, subtract angles

Answer 23

ok:) let me write it out.

Answer 24

er is 5/2(sq2) = -
[5(sq10)]/4?

Answer 25

5/4 sqrt(2)

Answer 26

the root cannot be in the base :o