Complex Numbers
Simplify the expression to a + bi form:
(−3−2i)−(11+10i)
−14−12i
Given the matrices A and B shown below, find A−B.
A = [[-1], [-5], [2]] , B= [[0], [3], [-1]]
[[-1], [-8], [3]]
Determine the y-intercept of the following equation.
(x+5)(x+1)=y
(0,5)
Solve for x:
sqrt(5x + 66 ) + 2 = 8
-6
In ΔEFG, g = 8.4 inches, m∠G=79° and m∠E=25°. Find the length of f, to the nearest 10th of an inch.
8.3
Write (−4+3i)2 in simplest a+bi form.
7−24i
Given the matrices A and B shown below, find 3B+A.
A = [[6,2], [1,5],[-3,1]] B = [[0,-2], [-5, -8], [0,0]]
[[6,4], [-14,-19], [-3,1]]
Factor completely.
16x2 + 56
8(2x2+7)
sqrt(17 -x) = x - 5
8
In ΔFGH, g = 910 cm, m∠G=98° and m∠H=51°. Find the length of h, to the nearest 10th of a centimeter.
714.2
If a=−3x and b=−2i, then find the value of the ab2 in fully simplified form.
12x
Find the product of the following two matrices.
[[2,1], [1,0]] [[-1,-5], [-3,1]]
[[-5,-9],[-1,-5]]
Factor.
x2 + 14x + 49
(x + 7)(x + 7)
Solve for x:
sqrt(x) -1 = sqrt(x-10)
30.25
In ΔWXY, w = 2.6 cm, x = 7.4 cm, and ∠Y=13°. Find the length of y, to the nearest 10th of a centimeter.
4.9
Express in simplest a+bi form:
(3+4xi)(4−3i)+(1−4xi)(4−3i)
16−12i
Find the determinant of the matrix
[[3,4], [-1,6]]
22
Factor the trinomial:
2x2 + 17x + 21
(2x+3)(x+7)
Solve for x:
sqrt (9x) + 2 = sqrt(x + 12)
1/4
In ΔDEF, f = 830 cm, d = 520 cm, and ∠E=129°. Find the length of e, to the nearest centimeter.
1226
Express (3/2 + 3/4 i)^2 in a+bi form, where a and b are written as fractions or integers in simplest terms.
27/16 + 9/4 i
Find the determinant of the matrix
[[-1,-5], [5,6]]
19
Factor completely.
2x2−32x4
2x2(1+4x)(1−4x)
Solve for all values of x:
sqrt(6x) +2 = sqrt (x+10)
6/25
In ΔRST, r = 7.5 cm, s = 7.1 cm, and t=2.3 cm. Find the measure of ∠S to the nearest degree.
71*