Convert the complex no. In polar form : 1-i

Question

rcosΘ =1
rsinΘ=-1
r=√a2+b2
r=√(1)2+(-1)2
r=√2

TanΘ=b/a
=1/-1
=-1

After all this what i have to do to find out value of Θ?
Please help me..

For polar form,
=r(cosΘ+isinΘ)

Answer 1

You are correct so far, r = √2
all you need is Ø, and you almost got it

tanØ = -1
we know that tan π/4 = +1, (tan 45° = 1)
and we also know that 1 - i would form an angle in quadrant IV
so Ø must be 2π - π/4 = 7π/4

so 1 - i = √2cos 7π/4 + √2sin 7π/4
or √2(cos 7π/4 + sin 7π/4)

Here is an excellent clip by Sal Khan
https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/polar-form-of-complex-numbers/v/polar-form-complex-number

Answer 2

Thanks for helping m

Answer 3

Thanks for helping me