Answer:
1∠22.5°, 1∠112.5°, 1∠202.5°, 1∠292.5°
Step-by-step explanation:
A root of a complex number can be found using Euler's identity.
<h3>Application</h3>
For some z = a·e^(ix), the n-th root is ...
z = (a^(1/n))·e^(i(x/n))
Here, we have z = i, so a = 1 and z = π/2 +2kπ.
Using r∠θ notation, this is ...
i = 1∠(90° +k·360°)
and
i^(1/4) = (1^(1/4))∠((90° +k·360°)/4)
i^(1/4) = 1∠(22.5° +k·90°)
For k = 0 to 3, we have ...
for k = 0, first root = 1∠22.5°
for k = 1, second root = 1∠112.5°
for k = 2, third root = 1∠202.5°
for k = 3, fourth root = 1∠292.5°
The percentage change is 36%
Answer:
His overall final score is 80.1.
His letter grade is a B.
Step-by-step explanation:
To find his grade, we multiply each grade by it's weight.
Grades and weights:
His midterm score is 64. The midterm counts 20% = 0.2.
His project score is 80. The project score counts 20% = 0.2.
His homework score is 94. The homework score counts 30%.
His final exam score is 77. It counts 30%.
What is his overall final score?
64*0.2 + 80*0.2 + 94*0.3 + 77*0.3 = 80.1
His overall final score is 80.1.
What letter grade did he earn (A, B, C, D, or F)?
At least 80 but less than 90 is a B. He scored 80.1, so his letter grade is a B.
