Adaptive Practice
Complex Numbers
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Question 1 of 10
⏱ 0:30
Easy
If \( z = 3 + 4i \), what is the modulus of \( z \)?
Easy
Find the conjugate of the complex number \( 7 - 2i \).
Easy
If \( z = 1 + i \), what is \( z^2 \)?
Medium
Which of the following represents the polar form of \( z = -1 + i \)?
Medium
If \( z_1 = 2 + 3i \) and \( z_2 = 1 - 4i \), find \( z_1 \cdot z_2 \).
Medium
If \( z = re^{i\theta} \), what is \( z^{-1} \)?
Easy
Solve for \( z \): \( z^2 + 1 = 0 \).
Medium
If \( z = \cos 60^\circ + i \sin 60^\circ \), find \( z^3 \) in trigonometric form.
Medium
Find the square roots of \( -16 \) in the form \( a + bi \).
Easy
If \( z = 1 + i \sqrt{3} \), find \( \arg(z) \) in degrees.