Solve the equationz^4 + 81 = 0

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- Jun 14th 2006, 04:21 AMnoriveaSolve the equation z^4 + 81 = 0
Solve the equation

*z*^4 + 81 = 0 - Jun 14th 2006, 04:43 AMtopsquarkQuote:

Originally Posted by**norivea**

Taking the square root of both sides:

Again taking the square root of both sides:

=

So what is ?

To answer this, let's write "i" a bit differently using the exponential form for complex numbers:

Thus

= = =

Similarly:

= ... =

So finally the solution to is

= and

-Dan - Jun 14th 2006, 05:23 AMSoroban
Hello, norivea!

Quote:

Solve the equation:

We have: .

The polar form of is: .

Then: .

Hence: . for

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Alternate method

We have: .

. . Then: . and

Now, if you*happen to know*that: .

. . then we have: . and

which gives us the same fourth roots.

- Jan 15th 2013, 11:08 AMTheSaviourRe: Solve the equation z^4 + 81 = 0

From here I trust you know how to solve quadratic equations (use the quadratic formula/complete the square). - Jan 15th 2013, 01:11 PMtopsquarkRe: Solve the equation z^4 + 81 = 0
- Jan 15th 2013, 01:16 PMTheSaviourRe: Solve the equation z^4 + 81 = 0