Question

Express the complex number in trigonometric form.

-2i

2(cos 180° + i sin 180°)
2(cos 90° + i sin 90°)
2(cos 270° + i sin 270°)
2(cos 0° + i sin 0°)

Answer 1

a+bi= 0+2i

Answer 2

how do we calculate the angle ??

Answer 3

also the value of r

Answer 4

\[r=\sqrt{a^2+b^2}\]

Answer 5

now you tell me abt how we cal angle??

Answer 6

one sec

Answer 7

use the formula you just said, right? If r is the angle then it is 4

Answer 8

r is not the angle

Answer 9

a+ib in trigonometric form
=\[r*(\cos \theta + i \sin \theta)\]

Answer 10

i don't know how to find the angle

Answer 11

\[\theta=\tan^{-1}\frac{ imaginary -part }{ real-part}\]

Answer 12

can u do it now ??

Answer 13

imaginary part=-2
real part= 0

Answer 14

yup

Answer 15

63.434

Answer 16

Wait, you can't divide by 0

Answer 17

anything divide by zero =???

Answer 18

undifined? 0?

Answer 19

undefined*

Answer 20

when tan becomes undefined???

Answer 21

cos(theta) = 0?

Answer 22

when cos gives 0 ???

Answer 23

i mean for what value of theta cos becomes 0??

Answer 24

90 and 270

Answer 25

well our imaginary part is negative so when there is negative in tan it will give negative output

Answer 26

so 270

Answer 27

yes :)

Answer 28

now trigo form =
r(cos theta + i sin theta )

Answer 29

tell me what you got ???

Answer 30

2(cos 270° + i sin 270°)

Answer 31

how to calculate r you already know

Answer 32

yes

Answer 33

cos 270=??

Answer 34

0

Answer 35

sin 270=???

Answer 36

you already got the ans

Answer 37

-1

Answer 38

this is for back conversion to a+i b form

Answer 39

2(0+i(-1))=-2i
so we are done :)

Answer 40

hope you wont face any difficulty in trigo or a+ib form conversion