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If ((1+i)/(1-i))^m=1, then find the leas...

If `((1+i)/(1-i))^m=1,` then find the least positive integral value of `mdot`

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The correct Answer is:
N/a
`(1 + i)/(1-i)=(1+ i)/(1- i)xx(1+ i)/(1+ i)`
` " "=(1+i^(2) +2i)/(1 -i^(2))=(1-1+2i)/(1+1)=i`
Now, ` ((1+i)/(1-i))^(m)=1`
`rArr" "i^(m)=1`
If `m` is positive, then
` " "m=4, 8, 12,...`
` therefore` Least positive value = 4
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NAGEEN PRAKASHAN ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATION -MISCELLANEOUS EXERCISE
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  7. Solve the equation :x^2-2x+3/2=0

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  9. Solve the following quadratic: 21 x^2-28 x+10=0

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  10. If z1=2-i ,z2=1+i ,find |(z1+z2+1)/(z1-z2+i)|

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  12. If z1=2-i ,\ +2=-2+i , find : R e((z1z2)/(z1))

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  13. Find the modulus and argument of the complex number (1+2i)/(1-3i).

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  15. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i)

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  16. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

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  17. If alphaand betaare different complex numbers with |beta|=1,then fin...

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  18. Find the number of non-zero integral solution of the equation |1-i|^x=...

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  20. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

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