Modulus / Magnitude / Absolute value of complex numbers Example-1

1. `A=5+6i`
Find Modulus / Magnitude / Absolute value of complex numbers

Solution:
Here `A=5+6i`

For a complex number `z=a+bi`, the modulus is `|z|=sqrt(a^2+b^2)`

`A=5+6i`

Here, `a=5,b=6`

`:. |A|=sqrt(5^2+6^2)=sqrt(25+36)=sqrt(61)=7.8102`

`:.` The modulus of `5+6i` is `7.8102`

2. `A=-2+3i`
Find Modulus / Magnitude / Absolute value of complex numbers

Solution:
Here `A=-2+3i`

For a complex number `z=a+bi`, the modulus is `|z|=sqrt(a^2+b^2)`

`A=-2+3i`

Here, `a=-2,b=3`

`:. |A|=sqrt((-2)^2+3^2)=sqrt(4+9)=sqrt(13)=3.6056`

`:.` The modulus of `-2+3i` is `3.6056`

3. `A=1-3i`
Find Modulus / Magnitude / Absolute value of complex numbers

Solution:
Here `A=1-3i`

For a complex number `z=a+bi`, the modulus is `|z|=sqrt(a^2+b^2)`

`A=1-3i`

Here, `a=1,b=-3`

`:. |A|=sqrt(1^2+(-3)^2)=sqrt(1+9)=sqrt(10)=3.1623`

`:.` The modulus of `1-3i` is `3.1623`

This material is intended as a summary. Use your textbook for detail explanation.
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