Question

# Find the modulus of each of the complex numbers 5i, 7, and 3 + 4i.

Complex numbers
Find the modulus of each of the complex numbers 5i, 7, and 3 + 4i.

2021-02-15
$$\displaystyle{\left|{z}\right|}=\sqrt{{{a}^{{2}}+{b}^{{2}}}}$$
therefore,the magnitude or modulus of the complex number 5i is:
we can write the complex number as 0+5i
therefore the magnitude or modulus of the complex number is $$\displaystyle\sqrt{{{0}^{{2}}+{5}^{{2}}}}=\sqrt{{{5}^{{2}}}}={5}$$
therefore the magnitude or modulus of complex number 5i is 5
the magnitude or modulus of the complex number 7 is:
we can write the complex number as 7+0i
therefore the magnitude or modulus of the complex number is $$\displaystyle\sqrt{{{7}^{{2}}+{0}^{{2}}}}=\sqrt{{{7}^{{2}}}}={7}$$
therefore the magnitude or modulus of complex number 7 is 7
the magnitude or modulus of the complex number 3+4i is:
therefore the magnitude or modulus of the complex number is $$\displaystyle\sqrt{{{3}^{{2}}+{4}^{{2}}}}=\sqrt{{{9}+{16}}}=\sqrt{{25}}={5}$$
therefore the magnitude or modulus of complex 3+4i is 5.