Class 11 Mathematics · Chapter 1 · Test 3
Polar Form and Euler
43 MCQs This test covers polar form, modulus and principal argument, Euler’s formula, and converting between polar and rectangular form. It also covers multiplication and division in polar form, loci, AC circuit impedance and complex-number cryptography.
43 questions · 35 min · 43 marks
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Sample questions
The first 5 of 43. Try each one, then tap to see the answer.
Question 1
For z = x + iy the modulus r equals:
- Ax + y
- Bsqrt(x^2 + y^2)
- Cx^2 + y^2
- Dsqrt(x^2 - y^2)
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Answer: B
r = |z| = sqrt(x^2 + y^2).
Question 2
In polar form y equals:
- Ar cos(theta)
- Br tan(theta)
- Cr sin(theta)
- Dr / sin(theta)
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Answer: C
x = r cos(theta) and y = r sin(theta).
Question 3
cos(theta) + i sin(theta) is written in short as:
- Ae^theta
- Bcis(theta)
- Ci theta
- De^(-i theta)
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Answer: B
cis(theta) = cos(theta) + i sin(theta).
Question 4
Euler's formula states that e^(i theta) equals:
- Acos(theta) + i sin(theta)
- Bcos(theta) - i sin(theta)
- Csin(theta) + i cos(theta)
- D1 + i theta
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Answer: A
e^(i theta) = cos(theta) + i sin(theta).
Question 5
The principal argument of a complex number lies in the interval:
- A[0, 2pi)
- B(-pi, pi]
- C(-pi/2, pi/2)
- D[0, pi]
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Answer: B
The principal argument satisfies -pi < arg z <= pi.
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