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If z = 2 − 3i, then z2 − 4z + 13 =
  • a)
    1
  • b)
    0
  • c)
    2
  • d)
    3
Correct answer is option 'B'. Can you explain this answer?
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If z = 2 − 3i, then z2 − 4z + 13 =a)1b)0c)2d)3Correct answ...
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If z = 2 − 3i, then z2 − 4z + 13 =a)1b)0c)2d)3Correct answ...
Understanding the Problem
To solve the equation z^2 - 4z + 13, where z = 2 - 3i, we will substitute the value of z into the equation and simplify.
Step 1: Calculate z²
- First, we find z²:
- z² = (2 - 3i)(2 - 3i)
- Using the formula (a - bi)² = a² - 2abi + (bi)²:
- = 4 - 12i + 9i²
- Since i² = -1:
- = 4 - 12i - 9
- = -5 - 12i
Step 2: Calculate -4z
- Next, we calculate -4z:
- -4z = -4(2 - 3i)
- = -8 + 12i
Step 3: Combine the components
Now, we can substitute z² and -4z into the equation:
- z² - 4z + 13:
- = (-5 - 12i) + (-8 + 12i) + 13
- Combine like terms:
- = (-5 - 8 + 13) + (-12i + 12i)
- = 0 + 0i
- = 0
Conclusion
The final result is 0. Hence, the correct answer is option 'B'. This shows that the expression z² - 4z + 13 simplifies perfectly to zero when z is substituted with 2 - 3i.
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