1 Given the complex number 1I a Find th Find the trigonometr

1. Given the complex number 1-I, (a) Find th Find the trigonometric form in the interval [0,2 r) and r > 0 ts. (b) Using your answer to part (a), find (1-i), and write the answer in standard complex form (a+b)

Solution

(1-i)

R= sqrt(1^2 +(-1)^2)=sqrt2

tan theta=-1/1=-1

theta = 7pi/4

required point is sqrt2 ( cos 7pi/4 +isin 7pi/4)

(1-i)^8= (sqrt2(cos7pi/4 +isin 7pi/4)^8=sqrt2^8(cos 8*7pi/4 +i sin 8*7pi/4)

= 16(cos 14pi +i sin 14pi)= 16(1 +0i)=16