CBSE Class 11-science Answered
find square root of 7+24i
Asked by tahikpreet0001 | 17 Apr, 2024, 06:41: AM
Expert Answer
Let z = 7 + i 24 = r [ cosα + i sinα ]
where r is modulus and α is argument of complex number
tan α = 24/7 and α = tan-1 ( 24/7 ) = 1.287 rad
Hence given complex number is
z = 25 [ cos α + i sin α ]
Square root of complex number is
z1/2 = 5 [ cos α + i sin α ]1/2 = 5 [ cos(α/2) + i sin(α/2) ]
z1/2 = 5 [ cos(0.6435) + i sin(0.6435) ] = 5 [ 0.8 + i 0.6 ] = 4 + i 3
Answered by Thiyagarajan K | 17 Apr, 2024, 12:11: PM
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