Consider z1 = a + bi and z2 = a - bi. Under what condition are z1 and z2 equal?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

Prepare for the A Level Further Mathematics Core Pure Exam. Practice with flashcards and multiple-choice questions, each accompanied by hints and explanations. Ace your exam!

Multiple Choice

Consider z1 = a + bi and z2 = a - bi. Under what condition are z1 and z2 equal?

Explanation:
If two complex numbers are equal, their real parts must be equal and their imaginary parts must be equal. Here both numbers have the same real part a, but the imaginary parts are b and -b. For equality, these imaginary parts must match, so b = -b, which means 2b = 0 and thus b = 0. When b = 0, both z1 and z2 reduce to a, so they are equal. Note that having a = 0 alone wouldn’t make them equal unless b is also 0.

If two complex numbers are equal, their real parts must be equal and their imaginary parts must be equal. Here both numbers have the same real part a, but the imaginary parts are b and -b. For equality, these imaginary parts must match, so b = -b, which means 2b = 0 and thus b = 0. When b = 0, both z1 and z2 reduce to a, so they are equal. Note that having a = 0 alone wouldn’t make them equal unless b is also 0.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy