Which of the following is the conjugate of the complex number z = 5 - 3i?

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Question: Which of the following is the conjugate of the complex number z = 5 - 3i?

Options:

Correct Answer: 5 + 3i

Solution:

The conjugate of a complex number z = a + bi is given by z* = a - bi. Here, the conjugate of 5 - 3i is 5 + 3i.

Which of the following is the conjugate of the complex number z = 5 - 3i?

Which of the following is the conjugate of the complex number z = 5 - 3i?

Step 1: Identify the complex number. In this case, the complex number is z = 5 - 3i.
Step 2: Recognize the format of a complex number, which is a + bi, where a is the real part and b is the imaginary part.
Step 3: In the given complex number, the real part (a) is 5 and the imaginary part (b) is -3.
Step 4: To find the conjugate, change the sign of the imaginary part. So, -3 becomes +3.
Step 5: Write the conjugate using the real part and the new imaginary part. The conjugate is 5 + 3i.

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