Test Session Chapter 1 Complex Numbers (1st Year Mathematics)

Multiple Choice Questions (MCQs)

Short Answer Questions

Important Formulas

Complex Number Form:

z = a + bi

where a = real part, b = imaginary part

i = √(-1)

Modulus:

|z| = √(a² + b²)

Conjugate:

Conjugate(z) = a – bi

Polar Form:

z = r(cos θ + i sin θ)

r = |z|, θ = arg(z)

Euler’s Formula:

z = r e^(iθ)

Complex Number Calculator

First Complex Number (z₁):

Second Complex Number (z₂):

Modulus & Argument Calculator

Complex Number (z):

Detailed Answer Questions

Question 1 (5 marks)

If z₁ = 2 + 7i and z₂ = -5 + 3i, then evaluate the following: | -7z₂ + 2z₂ |

Question 2 (5 marks)

Encrypt the word “CLASS” by adding the complex encryption key k = -3 + 4i. Then decrypt it back to the original word.

Question 3 (5 marks)

Solve the quadratic equation 2x² + 3x – 5 = 0 using completing square method.

Note: Answer any 2 questions. Each question carries 5 marks.

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