Blog eTrapez

There are days when nothing seems to work. And there are examples with complex numbers where nothing goes right. The known and memorized methods don’t help.

Take, for instance, this innocent-looking exponentiation: (1+2i)^8. Following the well-trodden path you’ve used in many examples, you want to write the number 1+2i in trigonometric form and then raise it to the eighth power using the appropriate formula. But you encounter complications along the way… See the trick I use.

Many fourth-degree polynomial equations can be transformed into quadratic equations using a well-known high school trick of substitution. This also works perfectly for polynomials in complex numbers.

See how to turn these equations into lower-degree equations.