solve 4z⁴+20z²=144 and represent in argand diagram

Question

argand diagram representation

Answer 1

4z^4+20z^2=144 simplifies to z^4+5z^2-36=0, which is a quadratic in z^2.

This factorises: (z^2-4)(z^2+9)=0, so there are two real solutions z^2-4=(z-2)(z+2) giving z=2 and z=-2.

z^2+9=0 has complex solutions z=3i and z=-3i, which are represented by the Argand diagram:

 

Comments

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