what is the solution to the inequality of cis greater than 6

Answer 1

cosx + isinx > 6

has no real solution

cosx < 1 if isinx =0, then cosx+isinx < 1 < 6

no real value of x will make it > 6

However, Euler's formula is e^ix = cisx = cosx + isinx

if cisx > 6, then e^ix > 6

take natural logs of both sides

ix > ln6

x > (ln6)/i

x is an imaginary number

ln6/i = iln6/-1 = -iln6 = the square root of -1 times negative ln6 where ln6 = about 1.8

x = about -1.8i