Identities (square, cube of 2 complex numbers)

Chapter 5 Class 11 Complex Numbers
Concept wise

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Ex 5.1, 10 Express the given Complex number in the form a + ib: (β2β1/3 π)^3 (β2β1/3 π)^3 = β 1 (2+1/3 π)^3 = β (2+1/3 π)^3 It is of the form (a + b)3 Using (a + b)3 = a3 + b3 + 3 ab (a + b) Here a = 2 and b = 1/3 i = β((2)^3+(1/3 π)^3+3 Γ2Γ1/3 π(2+1/3 π)) = β(8+(1/3)^3Γ(π)^3+2π(2+1/3 π)) = β(8+1/27 π^3+4π+2/3 π^2 ) = β(8+1/27 γπΓπγ^2+4π+2/3 π^2 ) Putting π^2=β1 = β1 (8+1/27 π(β1)+4π+2/3 (β1)) = β1 (8β1/27 π+4πβ2/3) = β 8 + 1/27 π β 4i + 2/3 = β 8 + 2/3 + ( 1)/27 π β 4π = (β 8+ 2/3) + (( 1)/27β4)π = ((β24 + 2)/3) + ((1 β 4 Γ27)/27)π = (β22)/3 + ((1 β108)/27)π = (β22)/3 + (( β107)/27)π = (β22)/3 β ( 107)/27 π