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

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

Question
Complex numbers
asked 2021-02-14
Find the modulus of each of the complex numbers 5i, 7, and 3 + 4i.

Answers (1)

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.
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