Complex Numbers

How do you add, subtract, multiply and divide complex numbers in Polar form?

1) Addition and subtraction is the same as vectors on an Argand diagram 2) To multiply - multiply the moduli and add the arguments 3) To divide - divide the moduli and subtract the arguments

How do you add, subtract, multiply and divide complex numbers in Cartesian form?

1) Addition, subtraction and multiplication is the same as for normal numbers 2) To divide multiply top and bottom of the fraction by the complex conjugate of the denominator

How to solve an equation involving complex numbers?

1) Change to Cartesian form 2) equate real and imaginary parts 3) solve as 2 simultaneous equations

What must be true for two complex numbers to be equal?

1) their real parts are equal 2) their imaginary parts are equal

What is a complex number?

A number that has a real component and an imaginary component.

What is De Moivre's theorem

A way of raising a complex number to a power

What is the imaginary part of the number z written as?

Im(z)

What is the real part of the number z written as?

Re(z)

What is the modulus of a complex number z = a + bi ?

also called *r*

What is the complex conjugate of a complex number: z = a + bi ?

complex conjugate is written as z* z* = a - bi

What is the Cartesian form of a complex number z with real part a and imaginary part b?

z = a + bi