Solve the following in cartesian form:

$\displaystyle z^4=16$

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- Feb 24th 2011, 02:48 AMjohnsy123Solving equations in cartesian form.
Solve the following in cartesian form:

$\displaystyle z^4=16$ - Feb 24th 2011, 02:52 AMProve It
$\displaystyle \displaystyle z^4 = 16$

$\displaystyle \displaystyle z^4 - 16 = 0$

$\displaystyle \displaystyle (z^2)^2 - 4^2 = 0$

$\displaystyle \displaystyle (z^2 - 4)(z^2 + 4) = 0$

$\displaystyle \displaystyle z^2 - 4 = 0$ or $\displaystyle \displaystyle z^2 + 4 = 0 $

$\displaystyle \displaystyle z^2 = 4$ or $\displaystyle \displaystyle z^2 = -4$

$\displaystyle \displaystyle z = \pm 2$ or $\displaystyle \displaystyle z = \pm 2i$.

So the solutions are $\displaystyle \displaystyle z = -2, z = 2, z = -2i, z = 2i$. - Feb 24th 2011, 02:55 AMmr fantastic