/สัปดาห์แบบทดสอบ #4915
❓ Complex Roots Challenge
10 คำถาม
Test your skills with complex numbers by solving an intriguing equation involving square roots. This quiz is perfect for students and enthusiasts of advanced algebra.
ความคืบหน้าของคะแนน
ถูกต้อง 0 จาก 10
ตอบแล้ว 0 จาก 10
คำถามที่ 1
What is a common first step when solving the equation √k + √-k = 15 in the complex plane?
A.
Assume k is a real number.
B.
Let √k = z.
C.
Square both sides immediately.
D.
Substitute k = x + yi.
คำถามที่ 2
If √k = z, what is √-k in terms of z, assuming principal roots and that √(-1) = i?
A.
z/i
B.
-z
C.
iz
D.
-iz
คำถามที่ 3
After substituting √k = z and √-k = iz, what is the resulting linear equation for z?
A.
z^2 - z = 15i
B.
z + iz = 15
C.
z - iz = 15
D.
z^2 + (iz)^2 = 15
คำถามที่ 4
From the equation z(1 + i) = 15, what is the first step to isolate z?
A.
Subtract i from both sides.
B.
Divide both sides by (1 + i).
C.
Multiply by (1 - i).
D.
Divide both sides by 15.
คำถามที่ 5
To simplify z = 15 / (1 + i), which expression should you multiply the numerator and denominator by?
A.
(1 + i)
B.
i
C.
(1 - i)
D.
-i
คำถามที่ 6
What is the value of z in the equation z = 15 / (1 + i)?
A.
-7.5 - 7.5i
B.
7.5 + 7.5i
C.
15 - 15i
D.
7.5 - 7.5i
คำถามที่ 7
If z = √k, and you've found z, how do you calculate k?
A.
k = z
B.
k = √z
C.
k = z^2
D.
k = 1/z
คำถามที่ 8
If z = a + bi, what is z^2?
A.
a^2 + b^2
B.
a^2 - b^2 + 2abi
C.
a^2 - b^2
D.
a^2 + b^2 - 2abi
คำถามที่ 9
Given z = 7.5 - 7.5i, what is the value of k = z^2?
A.
-112.5i
B.
112.5
C.
112.5i
D.
-112.5
คำถามที่ 10
If the problem specified that 'k' must be a real number, how many solutions would there be for √k + √-k = 15?
A.
Exactly one solution.
B.
Infinitely many solutions.
C.
Exactly two solutions.
D.
No real solutions.
พรอมต์: √k +√-k=15 finf k
