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Question
If z=4+i√7, then value of z3−4z2−9z+91 equals
If z=4+i√7, then value of z3−4z2−9z+91 equals
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Solution
The correct option is C −1
We have, z−4=i√7z2−8z=−23
z3−4z2−9z+91=z(z2−8z)+4(z2−8z)+23z+91=−23z−92+23z+91=−1
We have,
z−4=i√7
z2−8z=−23
z3−4z2−9z+91
=z(z2−8z)+4(z2−8z)+23z+91
=−23z−92+23z+91
=−1
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