Skip over navigation

Complex Numbers

Problems

Complex Roots

Polar Form of Complex Numbers

Problem : Find all roots, real and complex, of the following polynomial: x 2 + 4 .

x = {2ı, -2ı} .

Problem : Find all roots, real and complex, of the following polynomial: x 4 - x 3 - x 2 - x - 2 .

x = {2, -1,ı, - ı}

Problem : If is a root of a polynomial, what must one other root be?

The complex conjugate of must be a root also, so -3ı is also a root of the polynomial.

Problem : Find all roots, real and complex, of the following polynomial: x 3 +4x 2 + 25x + 100 .

x = { -4, 5ı, -5ı} .

Problem : Find all roots, real and complex, of the following polynomial: x 4 +2x 2 - 3 .

x = {1, -1,ı, - ı} .

Problem : Find all roots, real and complex, of the following polynomial: x 8 +2x 7 +4x 6 +8x 5 - x 4 -2x 3 -4x 2 - 8x .

x = {0, -2, -1, 1,ı, - ı, 2ı, -2ı} .

Follow Us