1.

Express the complex number in the form r(cos theta+isin theta)(ii)1-sin alpha +icos alpha

Answer»


Answer :`SQRT2(COS ((alpha)/(2))-sin((alpha)/2)[cos((pi)/(4)+(alpha)/(2)) +isin((pi)/(4)+(alpha)/(2))if 0<=alpha<(pi)/(2) -sqrt2(cos ((alpha)/(2))-sin((alpha)/2)[cos((alpha)/(2)-(3pi)/(4)) +isin((alpha)/(2)-(3pi)/(4))if (pi)/(2)<=alpha<(3pi)/(2) -sqrt2(cos ((alpha)/(2))-sin((alpha)/2)[cos((alpha)/(2)-(3pi)/(4)) +isin((alpha)/(2)-(3pi)/(4))if (3pi)/(2)<=alpha<(2pi)`


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