Argand diagrams

• $y$axis 


  imaginary
• $x$ axis


  real
• modulus

  $|z|=$$√x^2+$$y^2$
• 2π radians

  360 degrees
• principle argument

  $-π<θ ≤π$
• tan θ

  y divided by x (no signs)
• $z$ in the first quadrant


  arg$z =$$α$
• $z$ second quadrant


  arg$z$ $=$$π -α$
• $z$ third quadrant


  arg$z =$$-(π-α)$
• $z$ fourth quadrant


  arg$z=$$-α$
• $|z| =$$r$
• modulus argument form of$z$


  $z =$$r(cosθ+isinθ)$
• $|z1z2|$


  $|z1||z2|$
• arg$(z1z2)$=


  arg$z1$ + arg$z2$
• multiplication in modulus-argument form

  $r1r2(cos(θ 1+θ 2)+$$isin(θ 1+θ 2))$
• division in modulus-argument form

  $r1/r2 (cos(θ 1-θ 2)+$$isin(θ 1-θ 2))$