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.
JEE Main Complex Numbers and Quadratic Equations — practice questions — page 2
Explore 70 free Complex Numbers and Quadratic Equations questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 70.
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 →Quadratic discriminant — true or false?Read the answer and worked solution →Sort: does the quadratic have real or complex roots?Read the answer and worked solution →Match the complex number form to its representationRead the answer and worked solution →Match each complex number partRead the answer and worked solution →Key in the power of iRead the answer and worked solution →Real or imaginary?Read the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →The symbol i is defined as a solution of the equation:Read the answer and worked solution →A number of the form a plus ib with real a and b is called:Read the answer and worked solution →In the complex number a plus ib, the number a is called the:Read the answer and worked solution →In the complex number a plus ib, the number b is called the:Read the answer and worked solution →Two complex numbers are equal when their real parts match and their:Read the answer and worked solution →The non-negative real number written with bars around z is its:Read the answer and worked solution →Changing a plus ib into a minus ib gives the complex:Read the answer and worked solution →The plane in which complex numbers are plotted is the:Read the answer and worked solution →In the Argand plane, the x-axis is called the:Read the answer and worked solution →In the Argand plane, the y-axis is called the:Read the answer and worked solution →In the Argand plane, the modulus of a complex number is its distance from the:Read the answer and worked solution →Quadratics were earlier solved over the reals when the discriminant was:Read the answer and worked solution →Square roots of negative real numbers exist in the set of:Read the answer and worked solution →With a negative discriminant, quadratic solutions are found in the set of:Read the answer and worked solution →The theorem stated without proof about roots is the fundamental theorem of:Read the answer and worked solution →The Fundamental Theorem of Algebra says a polynomial equation has at least:Read the answer and worked solution →A polynomial equation of degree n has how many roots?Read the answer and worked solution →The symbol for the square root of minus one was first introduced by:Read the answer and worked solution →Hamilton regarded a complex number as an ordered pair of:Read the answer and worked solution →W. R. Hamilton lived from 1805 until: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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