Represent z = -4 in polar form.

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Multiple Choice

Represent z = -4 in polar form.

Polar form writes a complex number as z = r(cos θ + i sin θ) or z = r e^{iθ}, where r is the distance from the origin and θ is the angle from the positive real axis. For z = -4, the distance from the origin is |−4| = 4, so the radius is 4. The point lies on the negative real axis, which means the angle from the positive real axis is π radians (180 degrees). So the polar form uses r = 4 and θ = π, giving z = 4(cos π + i sin π) = 4(−1) = −4. Note that θ = −π would point in the same direction, but the conventional principal angle is π. The other options would give a different point or a different magnitude.

Polar form writes a complex number as z = r(cos θ + i sin θ) or z = r e^{iθ}, where r is the distance from the origin and θ is the angle from the positive real axis. For z = -4, the distance from the origin is |−4| = 4, so the radius is 4. The point lies on the negative real axis, which means the angle from the positive real axis is π radians (180 degrees). So the polar form uses r = 4 and θ = π, giving z = 4(cos π + i sin π) = 4(−1) = −4. Note that θ = −π would point in the same direction, but the conventional principal angle is π. The other options would give a different point or a different magnitude.

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