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✩ Answer:

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  [tex]\bold{Hello~}\\\bold{Your~answer~is~below!}[/tex]

✩ Step-by-step explanation:

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1.) [tex]6+7i[/tex]:

✺ The modulus of a complex number is:

  • [tex]a+bi[/tex] is [tex]\sqrt{a^2+b^2}[/tex]

✺ The modulus of [tex]6+7i[/tex] is:

  • [tex]\sqrt{85}[/tex] ≈ [tex]9.219544457[/tex]

2.) [tex]10 + 2i[/tex]:

✺ The modulus of a complex number is:

  • [tex]a+bi[/tex] is [tex]\sqrt{a^2+b^2}[/tex]

✺ The modulus of [tex]10 + 2i[/tex] is:

  • [tex]2\sqrt{26}[/tex] ≈ [tex]10.198039027[/tex]

3.) [tex]6+7i+10 + 2i[/tex]:

✺ Combine the real and imaginary parts in [tex]6+7i+10+2i[/tex]:

  • [tex]|6+10+(7+2)i|[/tex]

✺ Do the additions in [tex]6+10+(7+2)i[/tex]:

  • [tex]|16+9i|[/tex]

✺ Solve the complex modulus using the formula:

  • [tex]a+bi[/tex] is [tex]\sqrt{a^2+b^2}[/tex]

✺  The modulus of [tex]16+9i[/tex] is:

  • [tex]\sqrt{337}[/tex] ≈ [tex]18.357559751[/tex]

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