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# Complex Numbers

Question | Answer |
---|---|

What is the square root of negative 36? √-36 | √-36 = √36 x √-1 = 6 x i = 6i |

How about the negative square root of negative 36? -√-36 | -√-36 = -(√36 x √-1) = -6 x i = -6i |

Solve this equation (7 + 2i) + (2 + 4i) | (7 + 2i) + (2 + 4i) = (7 + 2) + (2 + 4)i = 9 + 6i |

Now we’ll try the same problem with a negative i (7 - 2i) + (2 + 4i) | (7 - 2i) + (2 + 4i) = (7 + 2) + (-2 + 4)i = 9 + 4i |

Subtraction is just as easy (7 + 4i) - (2 + 2i) | (7 + 2i) - (2 + 4i) = (7 - 2) + (2 - 4)i = 5 - 2i |

Don’t be fooled if there isn’t a second real number (7 + 2i) - (4i) | (7 + 2i) - (4i) = (7 - 0) + (- 4)i = 7 - 2i |

When multiplying complex numbers remember that the product rule for radicals doesn’t apply √-36 x √-49 | √-36 x √-49 = 6i x 7i = 42i2 = 42(-1) = -42 |

Here’s another multiplication example 6i(2 - 7i) | 6i(2 - 7i) = 12i – 42i2 = 12i – 42(-1) = 12i + 42 = 42 + 12i |

Remember the FOIL method? (2 - 7i)(4 + 3i) | (2 - 7i)(4 + 3i) = 8 + 6i - 28i – 21i2 = 8 – 22i - 21i2 = 8 – 22i - 21(-1) = 8 – 22i + 21 = 29 – 22i |

Conjugate is hard to say but we need it for division 2 + 4i / 3 – 6i | 2 + 4i / 3 – 6i = (2 + 4i x 3 + 6i) / (3 – 6i x 3 + 6i) = 6 + 12i + 12i + 24i2 / 9 + 18i – 18i – 36i2 = 6 + 24i + 24(-1) / 9 – 36(-1) = (-18 + 24i) / 45 = - 18/45 + 24i / 45 |

Created by:
csmatthews