CAIE A-Level Mathematics 3.9.2 Complex Arithmetic

Practise adding, multiplying and dividing Cartesian complex numbers, rationalising quotients and solving equations by substituting z = x + iy and equating components.

Exam points

expand products using i² = −1 and collect the real and imaginary components
multiply a quotient by the conjugate of its denominator and simplify into x + iy
substitute z = x + iy, equate components and combine with modulus or reality conditions

[Maximum number: 3]

The complex numbers u and v are defined by u=-4+2 i and v=3+i.

Find $\frac{u}{v}$ in the form x+i y, where x and y are real.

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3.9.2—Complex numbers question 1