Table of contents

17. Graphing Complex Numbers

Polar Form of Complex Numbers

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Multiple Choice

Convert the complex number $z=12\left(\cos90\degree+i・\sin90\degree\right)$ from polar to rectangular form.

$z=12i$

$z=12$

$z=1$

$z=i$

Verified step by step guidance

Identify the polar form of the complex number, which is given as z = 12(cos 90° + i sin 90°).

Recall that the polar form of a complex number is z = r(cos θ + i sin θ), where r is the magnitude and θ is the angle.

Convert the polar form to rectangular form using the formula: z = r(cos θ) + i(r sin θ).

Substitute r = 12 and θ = 90° into the formula: z = 12(cos 90°) + i(12 sin 90°).

Calculate the trigonometric values: cos 90° = 0 and sin 90° = 1, then substitute these values to find the rectangular form: z = 12(0) + i(12 * 1).

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Convert the complex number z=12(cos90°+i・sin90°)z=12\left(\cos90\degree+i・\sin90\degree\right)z=12(cos90°+i・sin90°) from polar to rectangular form.