Homework SourseFor questions 16 19 write each expression in the standard f
For questions 16 - 19, write each expression in the standard form for the complex number a + bi. ( 2 points each) ![For questions 16 - 19, write each expression in the standard form for the complex number a + bi. ( 2 points each) Solution16 ) [4(cos(7pi/9) +isin(7pi/9))]^3 z](/WebImages/15/for-questions-16-19-write-each-expression-in-the-standard-f-1024582-1761530309-0.webp "For questions 16 - 19, write each expression in the standard form for the complex number a + bi. ( 2 points each) Solution16 ) [4(cos(7pi/9) +isin(7pi/9))]^3 z")
Solution
16 ) [4(cos(7pi/9) +isin(7pi/9))]^3
z^n = r^n(cos(n*x) +i*sin(n*x) )
4^3(cos7pi/3 +isin7pi/3)
=64(0.5 +i0.866) = 32 +i*5.42
18) fifth root of z : z^1/5 = (5 -5sqrt3i)^1/5
In trigonomatric form : z = 10 angle = 2pi -tan^-1(5sqrt3/5) = 2pi -pi/3 5pi/3
z = 10(cos5pi/3 +i*sin5pi/3)
fifth root : z^1/5 = 10^1/5[cos(pi/3) +i*sin(pi/3)]
= 1.58(0.5 +isqrt3/2)]
= 0.79 +i*1.37
