Compute the magnitude of z = -3 − 3i.

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Multiple Choice

Compute the magnitude of z = -3 − 3i.

The magnitude of a complex number is its distance from the origin in the complex plane, found by the Pythagorean sum of its real and imaginary parts: |a + bi| = sqrt(a^2 + b^2). For z = -3 − 3i, the real part is -3 and the imaginary part is -3, so |z| = sqrt((-3)^2 + (-3)^2) = sqrt(9 + 9) = sqrt(18). This can be written as 3√2, but sqrt(18) is the exact form shown in the option.

The magnitude of a complex number is its distance from the origin in the complex plane, found by the Pythagorean sum of its real and imaginary parts: |a + bi| = sqrt(a^2 + b^2). For z = -3 − 3i, the real part is -3 and the imaginary part is -3, so |z| = sqrt((-3)^2 + (-3)^2) = sqrt(9 + 9) = sqrt(18). This can be written as 3√2, but sqrt(18) is the exact form shown in the option.

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