Singapore GCE A-Level · H2 Mathematics

Complex numbers

41 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 41 questions

Find the modulus of the complex number $z = 3 + 4 i$ .
Find the modulus of the complex number $z = 5 + 12 i$ .
Find the modulus of the complex number $z = 8 + 15 i$ .
Find the modulus of the complex number $z = 6 + 8 i$ .
Find the modulus of the complex number $z = 7 + 24 i$ .
Find the modulus of the complex number $z = 20 + 21 i$ .
Given that $z_{1} = 2 + 3 i$ and $z_{2} = 1 - 2 i$ , find $z_{1} z_{2}$ .
Given that $z_{1} = 3 - i$ and $z_{2} = 2 + 4 i$ , find $z_{1} z_{2}$ .
Given that $z_{1} = 1 + 5 i$ and $z_{2} = 3 + i$ , find $z_{1} z_{2}$ .
Given that $z_{1} = 4 + 2 i$ and $z_{2} = - 1 + 3 i$ , find $z_{1} z_{2}$ .
Given that $z_{1} = 2 - 3 i$ and $z_{2} = 5 + i$ , find $z_{1} z_{2}$ .
Given that $z_{1} = 3 + 3 i$ and $z_{2} = 1 - i$ , find $z_{1} z_{2}$ .
Express $\frac{- 1 + 3 i}{1 + i}$ in the form $a + bi$ .
Express $\frac{4 + 3 i}{1 + 2 i}$ in the form $a + bi$ .
Express $\frac{7 - i}{2 - i}$ in the form $a + bi$ .
Express $\frac{4 - 2 i}{1 + i}$ in the form $a + bi$ .
Express $\frac{4 + 8 i}{3 + i}$ in the form $a + bi$ .
Find the argument of $z = 1 + i$ , giving your answer in radians in the interval $(- π, π]$ .
Find the argument of $z = - 1 + i$ , giving your answer in radians in the interval $(- π, π]$ .
Find the argument of $z = - 1 - i$ , giving your answer in radians in the interval $(- π, π]$ .
Find the argument of $z = 1 - i$ , giving your answer in radians in the interval $(- π, π]$ .
Find the argument of $z = 2 i$ , giving your answer in radians in the interval $(- π, π]$ .
Find the argument of $z = - 3$ , giving your answer in radians in the interval $(- π, π]$ .
Find the argument of $z = - 5 i$ , giving your answer in radians in the interval $(- π, π]$ .
Solve the equation $z^{2} - 2 z + 10 = 0$ .
Solve the equation $z^{2} - 4 z + 29 = 0$ .
Solve the equation $z^{2} - 6 z + 25 = 0$ .
Solve the equation $z^{2} - 2 z + 65 = 0$ .
Solve the equation $z^{2} - 4 z + 5 = 0$ .
Solve the equation $z^{2} - 8 z + 97 = 0$ .
Evaluate $(1 + i)^{4}$ .
Evaluate $(1 + i)^{8}$ .
Evaluate $(1 - i)^{4}$ .
Evaluate $(i)^{6}$ .
Evaluate $(i)^{4}$ .
Evaluate $(1 + i)^{2}$ .
Evaluate $(1 - i)^{2}$ .
A quadratic equation with real coefficients has one root $ $2 + 3 i$ $. State the other root.
A quadratic equation with real coefficients has one root $ $1 + 4 i$ $. State the other root.
A quadratic equation with real coefficients has one root $ $3 + 2 i$ $. State the other root.
A quadratic equation with real coefficients has one root $ $- 1 + 5 i$ $. State the other root.

Complex numbers

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