Video: Identifying the Real and Imaginary Parts of Complex Numbers

If 𝑧 = 4 − 3𝑖, which of the following statements is correct? [A] Re(𝑧) = 4, Im(𝑧) = −3 [B] Re(𝑧) = −3, Im(𝑧) = −4 [C] Re(𝑧) = 4, Im(𝑧) = 3 [D] Re(𝑧) = −3, Im(𝑧) = 4 [E] Re(𝑧) = 3, Im(𝑧) = 4

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Video Transcript

If 𝑧 is equal to four minus three 𝑖, which of the following statements is correct? Is it A) the real part equals four and the imaginary part equals negative three? Is it B) the real part equals negative three and the imaginary part equals negative four? Is it C) the real part equals four and the imaginary part equals three? Option D) The real part equals negative three and the imaginary part equals four? Or option E) the real part equals three and the imaginary part equals four?

A complex number can be written in the form 𝑎 plus 𝑏𝑖, where 𝑎 and 𝑏 are real numbers. The first part of the number 𝑎 is the real part and the second part 𝑏𝑖 is the imaginary part. In our question, 𝑧 is equal to four minus three 𝑖. This means that four is the real part of the complex number 𝑧 and negative three is the imaginary part of the complex number 𝑧.

We can, therefore, conclude that the correct answer is option A. The complex number 𝑧 equals four minus three 𝑖 has a real part four and an imaginary part negative three.

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