Exponential (Euler) form
Practice Flashcards
Flip to reveal answersWhat is exponential (Euler) form?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Exponential (Euler) form
Sign up free to track progress and get spaced-repetition review schedules.
Question
What is exponential (Euler) form?
Answer
z = r e^(iθ), with r the modulus and θ the argument in radians.
Question
What is Euler's formula?
Answer
e^(iθ) = cosθ + i sinθ — it links the exponential form to the polar form.
Question
How do you multiply in exponential form?
Answer
Multiply the moduli and ADD the exponents: r₁r₂ e^(i(θ₁+θ₂)) (an index law).
Question
How do you divide in exponential form?
Answer
Divide the moduli and SUBTRACT the exponents: (r₁/r₂) e^(i(θ₁−θ₂)).
Question
Write 4 + 4i in exponential form.
Answer
r = 4√2, θ = π/4, so 4√2 e^(iπ/4).
Question
What is e^(iπ)?
Answer
−1 (so e^(iπ) + 1 = 0, Euler's identity).
Question
The three forms of a complex number?
Answer
Cartesian a + bi, polar r cisθ, exponential r e^(iθ) — all the same number.
Question
Why is the exponent written iθ, not θ?
Answer
Because e^(iθ) = cosθ + i sinθ; the i is essential — e^(θ) would be a real exponential.
Read the notes
Full study notes for Exponential (Euler) form
Topic 1.13 hub
Complex numbers: polar (HL only)
More from Topic 1.13
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free