Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it wi
multiply \\((9 - 11i)(-5 + 6i)\\). (1 point)
\\(\circ\\) \\(4 - 5i\\)
\\(\circ\\) \\(9 + 121i\\)
\\(\circ\\) \\(-111 + 109i\\)
\\(\circ\\) \\(21 + 109i\\)
check answer remaining attempts : 3

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first complex number by each term in the second:
$(9 - 11i)(-5 + 6i) = 9(-5) + 9(6i) - 11i(-5) - 11i(6i)$

Step2: Simplify each product

Calculate each term:
$9(-5) = -45$,
$9(6i) = 54i$,
$-11i(-5) = 55i$,
$-11i(6i) = -66i^2$.

Step3: Replace \(i^2\) with \(-1\)

Since \(i^2 = -1\), \(-66i^2 = -66(-1) = 66\).

Step4: Combine like terms

Combine real parts and imaginary parts:
Real: \(-45 + 66 = 21\)? Wait, no—wait, re - check Step1: Wait, no, 9(-5) is -45, -11i6i is -66i² = 66. Then real terms: -45 + 66? Wait, no, wait the first term is 9(-5) = -45, and the last term after replacing i² is +66. Then the middle terms: 54i + 55i = 109i. Wait, no, wait I made a mistake in Step1. Wait, (a + b)(c + d)=ac + ad + bc + bd. So (9 - 11i)(-5 + 6i)=9(-5)+9(6i)+(-11i)(-5)+(-11i)(6i). So 9(-5)= -45, 96i = 54i, -11i(-5)=55i, -11i6i = -66i². Now, i² = -1, so -66i² = -66(-1)=66. Now combine real parts: -45 + 66? Wait, no, that's wrong. Wait, no: 9(-5) is -45, and -11i6i is -66i² = 66. But also, wait, no, the first term is 9(-5)= -45, and the last term is +66. But wait, no, let's recalculate: Wait, 9(-5) = -45, -11i6i = -66i² = 66. Then real terms: -45 + 66? No, that can't be. Wait, no, I see the mistake. Wait, 9(-5) is -45, and -11i6i is -66i² = 66. But also, is there another real term? No, the real terms are 9(-5) and -11i6i (after replacing i²). The imaginary terms are 96i and -11i(-5). So real: -45 + 66 = 21? But the options have -111 + 109i. Wait, I must have messed up the signs. Wait, no! Wait, (9 - 11i)(-5 + 6i). Let's do it again. 9(-5) = -45, 9(6i)=54i, (-11i)(-5)=55i, (-11i)(6i)= -66i². Now, i² = -1, so -66i² = 66. Now, real parts: -45 + 66? No, that's 21, but the option 21 + 109i is there, but wait, no, wait I think I messed up the first multiplication. Wait, no, wait 9(-5) is -45, and -11i6i is -66i² = 66. Then -45 + 66 is 21, and 54i + 55i is 109i. So (9 - 11i)(-5 + 6i)=21 + 109i? But wait, the option is there: 21 + 109i. Wait, but let's check again. Wait, maybe I made a mistake in the sign of the first term. Wait, 9(-5) is -45, correct. -11i6i is -66i² = 66, correct. Then -45 + 66 = 21, correct. 54i + 55i = 109i, correct. So the product is 21 + 109i. Wait, but let's check with another method. Let's use (a - b)(-c + d)= -ac + ad + bc - bd. Wait, no, better to use the distributive property correctly. Wait, (9 - 11i)(-5 + 6i) = 9(-5) + 96i - 11i(-5) - 11i*6i = -45 + 54i + 55i - 66i². Now, i² = -1, so -66i² = 66. Then combine like terms: (-45 + 66) + (54i + 55i) = 21 + 109i. Yes, that's correct. Wait, but earlier I thought I made a mistake, but no. So the correct answer is 21 + 109i.

Answer:

21 + 109i (corresponding to the option "21 + 109i")