Question

someone want to help me multiply and divide complex numbers in polar form? :P
thanks :) ill give a medal and fan ^_^

Answer 1

go ahead and post the problem

Answer 2

given z=6(cos 108deg+isin108deg) and w=7(cos 26deg+isin26deg), find and simplify z/w. round numerical entries in the answer to two decimal places.

Answer 3

step by step how to please?

Answer 4

It turns out that there is a very handy formula when doing this in polar form

if

x = r1*cis(theta1)
y = r2*cis(theta2)

Then

x/y = (r1/r2)*cis(theta1 - theta2)

Answer 5

cis(theta) is shorthand for cos(theta) + i*sin(theta)

Answer 6

In this case,

z = 6*cis(108)
w = 7*cis(26)

Answer 7

So,

z/w = (6/7)*cis(108-26)

z/w = (6/7)*cis(82)

z/w = (6/7)*[cos(82) + i*sin(82)]

Answer 8

now use a calculator:

cos(82) = 0.13917310096007 (approximately)
sin(82) = 0.99026806874158

which means we can now say


z/w = (6/7)*[cos(82) + i*sin(82)]

z/w = (6/7)*[ 0.13917310096007+ i*0.99026806874158]

z/w = (6/7)*0.13917310096007+ (6/7)*i*0.99026806874158

z/w = 0.11929122939434 + 0.8488012017785i

z/w = 0.12 + 0.85i

Answer 9

thank you so much ^_^
do you know the formula for multiplying stuff like that too?

Answer 10

if

x = r1*cis(theta1)
y = r2*cis(theta2)

Then

x*y = (r1*r2)*cis(theta1 + theta2)

-----------------------------------------

if

x = r1*cis(theta1)
y = r2*cis(theta2)

Then

x/y = (r1/r2)*cis(theta1 - theta2)

Answer 11

There are the 2 (very related) rules together

Answer 12

thank you so so so so so so much!!!! :D

Answer 13

you're welcome