# Complex Number Equations

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Feb 27, 2022.

1. ### nycmathguy

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Section 6.6

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

nycmathguy, Feb 27, 2022
2. ### MathLover1

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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

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

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

Last edited: Feb 27, 2022
MathLover1, Feb 27, 2022
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3. ### nycmathguy

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nycmathguy, Feb 27, 2022
4. ### nycmathguy

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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.

nycmathguy, Feb 28, 2022
5. ### MathLover1

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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

MathLover1, Feb 28, 2022
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