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purely imaginary

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let z=m^2-m(1-i)-3(2+i),where m is a real number. If z is purely imaginary, find the value of m.

最佳解答:

z=m^2-m(1-i)-3(2+i) =m^2-m+im-6-3i =(m^2-m-6)+(m-3)i ∵z is purely imaginary,we have m^2-m-6 = 0 (m-3)(m+2) = 0 ∴m = 3 or m= -2

其他解答:

m^2 - m(1 - i) - 3(2 + i) =m^2 - m + mi - 6 - 3i =(m^2 - m - 6) - (m + 3)i Since z is purely imaginary, we have m^2 - m - 6 = 0. So, m = 3 or m = -2