Complex number image

Complex Numbers

Select an example from the list below:

Powers of i

Example 1: Basic powers of i


Example 2: Higher powers

a + i b numbers

Example 1: Adding and subtracting


Example 2: Multiplying


Example 3: Dividing

Argand diagram - Geometric problems

Example 1: Modulus and argument


Example 2: a + ib numbers


Example 3: Addition


Example 4: Subtraction


Example 5: Multiplication


Example 6: Powers


Example 7: Powers


Example 8: Distance/locus


Example 9: Inverse/reciprocal


Example 10: A proof about modulus and complex conjugate

Polar form

Example 1: r(cosθ + isinθ)


Example 2: Multiplication


Example 3: Division

De Moivre's theorem

Example 1


Example 2


Example 3: Powers

Roots of complex number

Example 1


Example 2: Roots of Unity


Example 3: Roots of -1


Example 4: Roots of Unity

Log of complex number

Example 1

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