1. `A=5+6i,B=-2+3i,C=1-3i`
Find |A|Solution:Here `A=5+6i,B=-2+3i,C=1-3i`
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=5+6i,B=-2+3i,C=1-3i`
Find |B|Solution:Here `A=5+6i,B=-2+3i,C=1-3i`
For a complex number `z=a+bi`, the modulus is `|z|=sqrt(a^2+b^2)`
`B=-2+3i`
Here, `a=-2,b=3`
`:. |B|=sqrt((-2)^2+3^2)=sqrt(4+9)=sqrt(13)=3.6056`
`:.` The modulus of `-2+3i` is `3.6056`
3. `A=5+6i,B=-2+3i,C=1-3i`
Find |C|Solution:Here `A=5+6i,B=-2+3i,C=1-3i`
For a complex number `z=a+bi`, the modulus is `|z|=sqrt(a^2+b^2)`
`C=1-3i`
Here, `a=1,b=-3`
`:. |C|=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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