Complex Split Exit Ticket
Algebra 2 Exit Ticket • Division & Conjugates
Dividing Complex Numbers
Score
/ 10
Name:
Date:
Period:
Directions: Multiply by the conjugate of the denominator, evaluate \(i^2 = -1\), and express in standard form \(a + bi\).
1
Simplify and write in standard form \(a + bi\):
\( \frac{5 + 2i}{3 - 4i} \) 5 pts
Show algebraic work:
Final Answer (\(a + bi\)):
2
Simplify completely and reduce all fractions:
\( \frac{8 - 4i}{3 + i} \) 5 pts
Show algebraic work:
Final Answer (\(a + bi\)):
Confidence Level:
1 - Need Help 2 - Almost There 3 - Got It
Alg2 • Form A
Honors Algebra 2 Advanced Exit Ticket • Radicals & Parameters
Dividing Complex Numbers
Score
/ 10
Name:
Date:
Period:
Directions: Rationalize exact radical coefficients, justify parameter values algebraically, and express answers in standard form \(a + bi\).
1
Divide and write in exact standard form \(a + bi\):
\( \frac{3 + i\sqrt{2}}{2 - i\sqrt{2}} \) 5 pts
Show complete algebraic steps with simplified radicals:
Exact Standard Form:
2
Find real constant \(k\) so \(z\) is pure imaginary (\(\text{Re}(z) = 0\)):
\( z = \frac{k + 6i}{3 - 2i} \) 5 pts
Show algebraic derivation for \(k\) and state the resulting quotient \(z\):
Value of \(k\):
Quotient \(z\):
Key Insight: Conjugate multiplication guarantees \((c+di)(c-di) = c^2 + d^2 \in \mathbb{R}\).
Honors Alg2 • Form H
