Perform the complex number division below:

8 | |

3 + 4i |

Complex number division involves multiplying numerator and denominator by the

If the denominator is c + di, the conjugate is c - di. Multiplying top and bottom by the conjugate (3 - 4i), we get:

(8)(3 - 4i) | |

(3 + 4i)(3 - 4i) |

The formula for this using the FOIL method is: (a * c) + (b * c) + (a * d) + (b * d) where:

a = 3, b = 4, c = 3, and d = -4

(3 + 4i)(3 - 4i) = (3 * 3) + (4i * 3) + (3 * -4i) + (4i * -4i)

(3 + 4i)(3 - 4i) = 9 + 12i - 12i - 16i

(3 + 4i)(3 - 4i) = 9 + (12 - 12)i - 16i

(3 + 4i)(3 - 4i) = 9 - 16i

i

(3 + 4i)(3 - 4i) = 9 - 16* (-1)

(3 + 4i)(3 - 4i) = 9 + 16

(3 + 4i)(3 - 4i) = (9 + 16)

(3 + 4i)(3 - 4i) =

The formula for this using the FOIL method is: (a * c) + (b * c) + (a * d) + (b * d) where:

a = 8, b = 0, c = 3, and d = -4

(8)(3 - 4i) = (8 * 3) + (8 * -4i)

(8)(3 - 4i) = 24 - 32i

(8)(3 - 4i) =

8 | |

3 + 4i |

= |

24 - 32i |

25 |

This fraction cannot be reduced down anymore, so we have our answer

8 | |

3 + 4i |

= |

24 - 32i |

25 |