Complex Numbers

Rationalize Denominator: Multiply numerator and denominator by the conjugate of the denominator $(1 - i)$ :
- $\frac{3 - 2 i}{1 + i} \times \frac{1 - i}{1 - i}$
Calculation:
- Numerator: $(3 - 2 i) (1 - i) = 3 - 3 i - 2 i + 2 i^{2} = 3 - 5 i - 2 = 1 - 5 i$ .
- Denominator: $(1 + i) (1 - i) = 1^{2} - i^{2} = 1 + 1 = 2$ .
Standard Form: The value is $\frac{1 - 5 i}{2} = \frac{1}{2} - \frac{5}{2} i$ .
Find Conjugate: The conjugate changes the sign of the imaginary part.
- $Conjugate = \frac{1}{2} + \frac{5}{2} i = \frac{1 + 5 i}{2}$ .

This medium difficulty mathematics question is from the chapter complex numbers and quadratic equations, covering the topic of complex numbers. It appeared in the 2025 exam.

Looking for more practice? Explore all mathematics questions or browse complex numbers and quadratic equations questions on RankGuru.

Complex Numbers

Select the correct option:

🔒 Solution Hidden from View

More complex numbers and quadratic equations Practice Questions

If z = 3 + 4i, then |z| equals

The argument of the complex number z = 1 + i is

If z₁ = 2 + 3i and z₂ = 1 - 2i, then z₁ × z₂ equals

If i = √(-1), then i⁴ + i⁸ + i¹₂ + i¹⁶ equals

If |z - 2| = 2|z - 1|, then the locus of z is

If z = cos θ + i sin θ, then z^n + 1/z^n equals

The cube roots of unity are

If ω is a cube root of unity, then (1 + ω - ω²)⁶ equals

If z is a complex number such that |z| = 1, then the value of (1 + z)/(1 + z̄) (where z̄ is the conj...

The set of all complex numbers z satisfying the equation given by the ratio condition arg of the qua...

If the equation x^2 - (k - 3)x + k = 0 has both roots real, then the set of all real values of the p...

Among all complex numbers z lying on the circle defined by |z| = 1, the maximum value attained by th...

About This Question

Solution