Consider z1 = a + bi and z2 = a - bi. Under what condition are z1 and z2 equal?

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Multiple Choice

Consider z1 = a + bi and z2 = a - bi. Under what condition are z1 and z2 equal?

Explanation:
If two complex numbers are equal, their real parts must be equal and their imaginary parts must be equal. Here both numbers have the same real part a, but the imaginary parts are b and -b. For equality, these imaginary parts must match, so b = -b, which means 2b = 0 and thus b = 0. When b = 0, both z1 and z2 reduce to a, so they are equal. Note that having a = 0 alone wouldn’t make them equal unless b is also 0.

If two complex numbers are equal, their real parts must be equal and their imaginary parts must be equal. Here both numbers have the same real part a, but the imaginary parts are b and -b. For equality, these imaginary parts must match, so b = -b, which means 2b = 0 and thus b = 0. When b = 0, both z1 and z2 reduce to a, so they are equal. Note that having a = 0 alone wouldn’t make them equal unless b is also 0.

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