Complex Number Equations

Section 6.6

Can you do 91 and 93 as a guide for me to do a few more? Thank you.

 

91
\(x^4+16i=0\)

\(x^4=-16i\)





solutions are:

\(x = 2cos(π/8) - 2i *sin(π/8)\)

\(x = 2cos(-π/8) + i *sin(-π/8)\)


93

\(x^3-(1-i)=0\)

\(x^3=(1-i)\)

 

For 92 and 94, I need a step by step solution starting where I got stuck. Thank you. This completes Chapter 6 for us. I was going to skip Chapters 7 through 9 but decided that this is a bad idea. Chapter 7 begins next Friday. Back to work tomorrow. My weekend is over.

 

88.
from here




90.

that is real solution, but we also have two complex solutions




92.
x^6+64*i=0
x^6= -64*i

For z^n=a the solutions are :



k=0,1,..... ,n-1
for n=6, a=-64i

substituting values for a, n, and k you will get following complex solutions:












94. doing this one using same method as in 92, solutions will be

 

I don't understand this complex equation stuff. I never studied this material back in my college days. Looks terribly advanced for precalculus students. What is the name of the course that goes into great detail concerning such equations? I took precalculus back in 1993. The professor did not teach this stuff.