Complex No. (1 Viewer)

[Parvee]

w^7=4+4i
Find the complex number w , lying in the third quadrant, and having the smallest possible real part, which satisfies the equation. Leave your answer in polar form.

I keep getting the wrong answer

 

[asianese]

w^7 = r^7cis7X = 4(1+i)=4*Sqrt2(cis pi/4+2piK)

equate modulus and arguments

X = pi/28 + 2piK/7, k integer

then sub in integer values for K, getting X = pi/28, 9pi/28, 17pi/28, 25pi/28, -pi/4, -15pi/28, -23pi/24 (check these they might be wrong)

then find the ones in 3rd quadrant, -15pi/28, -23pi/24 are there.

Re(w) = r*cosX, so just sub in cos of -15pi/28 and -23pi/24 and see which is smaller.

Soz about the bad typeset..not that bothered lol

 

[Parvee]

Oh I realised what I did wrong

Thanks

 

[asianese]

Nws m9