Revision sheet · Mathematics

Complex numbers

Modulus of a complex number: $∣ z ∣ = a^{2} + b^{2}$
Multiplying complex numbers: $(a + ib) (c + i d) = (a c - b d) + i (a d + b c)$
A complex number times its conjugate: $(a + ib) (a - ib) = a^{2} + b^{2}$
Dividing complex numbers: $\frac{a + ib}{c + i d} = \frac{( a c + b d ) + i ( b c - a d )}{c ^{2} + d ^{2}}$