Chapter 25 Multiple choice questions

* not completed

. Write the following complex number in the form a + bi:
$18-\sqrt{-81}$.

$18+9\text{i}$ correct incorrect

$18-9\text{i}$ correct incorrect

$27+0\text{i}$ correct incorrect

$0+9\text{i}$ correct incorrect

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. Simplify the following expression:
$\left(20-4\text{i}\right)-\left(6-5\text{i}\right)+\left(2\text{i}-3a\right)$.

$6-3a+23\text{i}$ correct incorrect

$14-3a+3\text{i}$ correct incorrect

$-3a+18\text{i}$ correct incorrect

$26-3a-7\text{i}$ correct incorrect

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. Multiply the following complex numbers:
(7 − 5i)(6 + 4i).

62 + 2i correct incorrect

21 − 2i correct incorrect

21 + 2i correct incorrect

62 − 2i correct incorrect

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. Multiply the following complex numbers:
(2c³ + 9pi)(5mc − 4p³i).

10 c⁴p − 36 p⁴+ cp²(45 − 8c²p) i correct incorrect

10 c⁴p − 36 p⁴+ cp²(45 + 8c²p) i correct incorrect

2p (5 c⁴ + 18 p³) + cp²(45 − 8c²p) i correct incorrect

2p (5 c⁴ + 18 p³) + cp²(8c²p − 45) i correct incorrect

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. Multiply the following complex numbers:
$2\left(\cos 4a+\text{i}\sin 4a\right)\times 7\left(\cos 3c+\text{i}\sin 3c\right)$.

$14\left(\cos 4a\cos 3c+\text{i}\sin 4a\sin 3c\right)$ correct incorrect

$14\left(\cos \left(4a+3c\right)+\text{i}\sin \left(4a+3c\right)\right)$ correct incorrect

$14\left(\cos 4a\sin 3c+\text{i}\cos 4a\sin 3c\right)$ correct incorrect

$14\left(\cos 4a\sin 3c+\text{i}\sin 4a\cos 3c\right)$ correct incorrect

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. Write the complex conjugate of $3c-4d\text{i}$.

$3c+4d\text{i}$ correct incorrect

$-4d\text{i}+3c$ correct incorrect

$3c\text{i}-4d$ correct incorrect

$3c\text{i}+4d$ correct incorrect

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. Simplify the following expression:
$\frac{12-6\text{i}}{4+3\text{i}}$.

$1.2+2.4\text{i}$ correct incorrect

$\frac{30}{7}+\frac{60}{7}\text{i}$ correct incorrect

$\frac{30}{7}-\frac{60}{7}\text{i}$ correct incorrect

$1.2-2.4\text{i}$ correct incorrect

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. Simplify the following expression:
$\frac{5-3z\text{i}}{9-4\text{i}}$.

$\frac{1}{65}\left(45+12z+\left(20-27z\right)\text{i}\right)$ correct incorrect

$\frac{1}{65}\left(45+12z-\left(20-27z\right)\text{i}\right)$ correct incorrect

$\frac{1}{97}\left(45+12z+\left(20-27z\right)\text{i}\right)$ correct incorrect

$\frac{1}{97}\left(45+12z-\left(20-27z\right)\text{i}\right)$ correct incorrect

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. Rewrite the following expression:
$h\cos 3a\theta +\text{i}h\sin 3a\theta$.

$h{\text{e}}^{3a\theta \text{i}}$ correct incorrect

$h{\text{e}}^{3a\theta }$ correct incorrect

$3h{\text{e}}^{3a\theta \text{i}}$ correct incorrect

$ah{\text{e}}^{3\theta }$ correct incorrect

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. Calculate
${\left(\cos 3\theta +\text{i}\sin 3\theta \right)}^5$.

$\cos \left(5\theta \right)+\text{i}\sin \left(5\theta \right)$ correct incorrect

$\cos \left(15\theta \right)+\text{i}\sin \left(15\theta \right)$ correct incorrect

${\cos }^{5}3\theta +\text{i}{\sin }^{5}3\theta$ correct incorrect

$3\left({\cos }^5\theta +\text{i}{\sin }^5\theta \right)$ correct incorrect