UniGeniusA-level Further Maths · Edexcel 9FM0

CP 2.1, CP 2.2

Complex numbers and quadratic roots

2 marksCore techniqueShow full working

Express

(2 + 3i)(4 - i)

in the form

a + bi

.

[2]

2 marksCore techniqueShow full working

Express

(5 - 2i)(3 + 4i)

in the form

a + bi

.

[2]

2 marksCore techniqueShow full working

Express

(-1 + 4i)(2 + 3i)

in the form

a + bi

.

[2]

3 marksCore techniqueShow full working

Express

\dfrac{5 - 5i}{3 + i}

in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Express

\dfrac{8 - i}{1 - 2i}

in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Express

\dfrac{-5 - i}{2 + 3i}

in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Express

\dfrac{5 + 3i}{1 + i}

in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Solve

z^2 - 4z + 29 = 0

, giving your answers in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Solve

z^2 + 6z + 10 = 0

, giving your answers in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Solve

2z^2 - 2z + 5 = 0

, giving your answers in the form

a + bi

.

[3]

3 marksCore techniqueShow full working

Solve

z^2 + 2z + 17 = 0

, giving your answers in the form

a + bi

.

[3]

5 marksCore techniqueShow full working

Find the square roots of

3 + 4i

.

[5]

5 marksCore techniqueShow full working

Find the square roots of

-5 + 12i

.

[5]

5 marksCore techniqueShow full working

Find the square roots of

-7 - 24i

.

[5]