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If z = 1 + i√3, find the conjugate of z.

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Question: If z = 1 + i√3, find the conjugate of z.

Options:

  1. 1 - i√3
  2. 1 + i√3
  3. 1 + √3i
  4. 1 - √3i

Correct Answer: 1 - i√3

Solution: 

The conjugate of a complex number z = a + bi is given by z* = a - bi. Thus, the conjugate of z = 1 + i√3 is 1 - i√3.

If z = 1 + i√3, find the conjugate of z.

Practice Questions

Q1
If z = 1 + i√3, find the conjugate of z.
  1. 1 - i√3
  2. 1 + i√3
  3. 1 + √3i
  4. 1 - √3i

Questions & Step-by-Step Solutions

If z = 1 + i√3, find the conjugate of z.
  • Step 1: Identify the complex number z. Here, z = 1 + i√3.
  • Step 2: Recognize that a complex number is in the form a + bi, where a is the real part and bi is the imaginary part.
  • Step 3: In our case, a = 1 and b = √3.
  • Step 4: The formula for the conjugate of a complex number z = a + bi is z* = a - bi.
  • Step 5: Apply the formula to find the conjugate: z* = 1 - i√3.
  • Step 6: Write down the final answer: The conjugate of z = 1 + i√3 is 1 - i√3.
  • Complex Conjugate – The conjugate of a complex number is obtained by changing the sign of the imaginary part.
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