The modulus of the complex number [tex]6+7i[/tex] is [tex]\sqrt{85}[/tex] and the modulus of the complex number [tex]2-3i[/tex] is [tex]\sqrt{13}[/tex].
How to find the modulus of complex number?
The modulus of a complex number is equal to the square root of the sum of the real part of the number and the imaginary part of the number.
It can be given as,
[tex]|Z|=\sqrt{x^2+y^2}[/tex]
Here, [tex]x[/tex] is the real part of the complex number and [tex]y[/tex] is the imaginary part of the complex number.
Given information-
- A) The complex number given in the problem for part A is,
[tex]6+7i[/tex]
Here in the above number the real part of the complex number is 6.
The imaginary part of the complex number is 7.
Find the modulus of the given complex number using the above formula as,
[tex]|Z|=\sqrt{6^2+7^2}\\|Z|=\sqrt{36+49}\\|Z|=\sqrt{85}[/tex]
- B) The complex number given in the problem for part B is,
[tex]2-3i[/tex]
Here in the above number the real part of the complex number is 2.
The imaginary part of the complex number is -3.
Find the modulus of the given complex number using the above formula as,
[tex]|Z|=\sqrt{2^2+(-3)^2}\\|Z|=\sqrt{4+9}\\|Z|=\sqrt{13}[/tex]
Hence the modulus of the complex number [tex]6+7i[/tex] is [tex]\sqrt{85}[/tex] and the modulus of the complex number [tex]2-3i[/tex] is [tex]\sqrt{13}[/tex].
Learn more about the modulus of complex number here;
https://brainly.com/question/25925813
