alleryThe value of (1 + i)/(1 − i) is
- −i
- −1
- 1
- i
Show answer and solution
Correct answer: D. i
Multiply num and denom by (1+i): (1+i)²/((1)²+(1)²) = 2i/2 = i.
AP Intermediate 1st Year Complex Numbers and Quadratic Equations — practice questions — page 2
Explore 46 free Complex Numbers and Quadratic Equations questions in AP Intermediate 1st Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–46 of 46.
The value of (1 + i)/(1 − i) isRead the answer and worked solution →|z₁ z₂| equalsRead the answer and worked solution →In z = a + ib, Re(z) and Im(z) areRead the answer and worked solution →The complex number i is defined by:Read the answer and worked solution →For the complex number z = 2 + 5i, Re z and Im z are:Read the answer and worked solution →The conjugate of the complex number z = 2 - 5i is:Read the answer and worked solution →If 4x + i(3x - y) = 3 + i(-6), then x and y are:Read the answer and worked solution →Compute (3 + 5i)(2 + 6i).Read the answer and worked solution →What is i^35?Read the answer and worked solution →The modulus |3 + i| equals:Read the answer and worked solution →The multiplicative inverse of z = 2 - 3i is:Read the answer and worked solution →Express (5 + √2 i)/(1 - √2 i) in the form a + ib.Read the answer and worked solution →Find the value of i^(-39).Read the answer and worked solution →Compute (5 - 3i)³.Read the answer and worked solution →If x + iy = (a + ib)/(a - ib), then x² + y² equals:Read the answer and worked solution →Identify the standard form of (-i)(2i)(-i/8)³.Read the answer and worked solution →
Worked practice questions
|z₁ z₂| equals
- |z₁||z₂|
- |z₁|/|z₂|
- |z₁|−|z₂|
- |z₁|+|z₂|
Show answer and solution
Correct answer: A. |z₁||z₂|
The modulus is multiplicative: |z₁z₂| = |z₁||z₂|.
In z = a + ib, Re(z) and Im(z) are
- a and ib
- b and a
- a and b
- ib and a
Show answer and solution
Correct answer: C. a and b
Re(z) = a (real part), Im(z) = b (imaginary part, the real coefficient of i).
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