Convert the complex number 4-7i into polar form

The polar form of the nonzero complex number is denoted as z = r(cos(θ) + isin(θ)) where a = rcos(θ) and b = rsin(θ) and r = √a

In this case, a = 4 and b = -7

r = √a

r = √4

r = √16 + 49

r = √65

r = 8.5

From above, a = rcos(θ), so we have:

cos(θ) = | a |

r |

cos(θ) = | 4 |

8.5 |

cos(θ) = 0.83

From above, b = rsin(θ), so we have:

sin(θ) = | b |

r |

sin(θ) = | -7 |

8.5 |

sin(θ) = -0.46

tan(θ) = | sin(θ) |

cos(θ) |

tan(θ) = | -0.46 |

0.83 |

tan(θ) = -1.75

θ = arctan(-1.75)

θ = -4

z = r(cos(θ) + isin(θ))

z =