Question

Find each absolute value

| 4+2i |

| 5-i |

| -3i |

Answer 1

Well it would stay the same since you need to have i to equal something

Answer 2

How to get answer for number 1: | 4+2i |

`\left|a+bi\right|\:=√(\left(a+bi\right)\left(a-bi\right))=√(a^2+b^2)\\\mathrm{With\:}a=4,\:b=2\\=√(4^2+2^2)\\Refine\\=√(20)\\√(20)=2√(5)\\=2√(5)`

How to get answer for number 2: | 5-i |

`\left|a+bi\right|\:=√(\left(a+bi\right)\left(a-bi\right))=√(a^2+b^2)\\\mathrm{With\:}a=5,\:b=-1\\=√(5^2+\left(-1\right)^2)\\=√(26)`

Number 3 how to get answer: | -3i |

`\left|a+bi\right|\:=√(\left(a+bi\right)\left(a-bi\right))=√(a^2+b^2)\\\mathrm{With\:}a=0,\:b=-3\\=√(0^2+\left(-3\right)^2)\\Refine\\=√(9)\\√(9)\\\mathrm{Factor\:the\:number:\:}\:9=3^2\\=√(3^2)\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a\\√(3^2)=3\\= 3`