Question 1

${i^{54}}$

Accepted Answer

$-1$

Answer

$-i$

Answer

1

Answer

$i$

Question 2

Evaluate: ${i^{103}}$

Accepted Answer

$-i$

Answer

$-1$

Answer

$i$

Answer

1

Question 3

Simplify:  $4\sqrt -36$

Accepted Answer

$24i$

Answer

$-24$

Answer

$-24i$

Answer

$4\sqrt 6 i$

Question 4

Simplify:  $ - 5\sqrt -23 $

Accepted Answer

$ - 5\sqrt {23} i$

Answer

$5\sqrt {23} i$

Answer

$ - 15\sqrt {23} i$

Answer

$-115i$

Question 5

Simplify and write in standard form: $7 - \sqrt-18 $

Accepted Answer

$7 - 3\sqrt 2 i$

Answer

$4\sqrt 2 i$

Answer

$5\sqrt 3 i$

Answer

$7 + 2\sqrt 3 i$

Question 6

Simplify and write in standard form: $(8 - 17i) + ( - 2 + 13i)$

Accepted Answer

$6 - 4i$

Answer

$16 + 221i$

Answer

$2i$

Answer

$-16 +221i$

Question 7

Simplify and write in standard form: $(-10 +3i) - ( -5 + i)$

Accepted Answer

$-5+2i$

Answer

$-5+4i$

Answer

$50+3i$

Answer

$-15+4i$

Question 8

Simplify and write in standard form: $(3i) - ( -5i)$

Accepted Answer

$8i$

Answer

$-15i$

Answer

$15$

Answer

$-2i$

Question 9

Simplify and write in standard form: $(3 - i)(4 - 2i)$

Accepted Answer

$10-10i$

Answer

$10-2i$

Answer

$14-10i$

Answer

$14-2i$

Question 10

Find the $x$ and $y$ values:  $3x +10yi = 21 - 5i$

Accepted Answer

$x=7$ and $y = - \frac{1}{2}$

Answer

$x = -7$ and $y = \frac{1}{2}$

Answer

$x=7$ and $y = -2$

Answer

$x=6$ and $y=-2$

Question 11

Evaluate: $5{i^2}$

Accepted Answer

$-5$

Answer

5

Answer

$-25$

Answer

$5i$

Question 12

Evaluate: $ - 7{i^3}$

Accepted Answer

$7i$

Answer

$343i$

Answer

$-7i$

Answer

7

Question 13

Simplify and write in standard form: $4{i^2}(7 - 8i)$

Accepted Answer

$-28+32i$

Answer

$28-32i$

Answer

$-32-28i$

Answer

$32+28i$

Question 14

Identify the complex conjugate: $-19 + 21i$

Accepted Answer

$-19 - 21i$

Answer

$-21 + 19i$

Answer

$19 - 21i$

Answer

$19 + 21i$

Question 15

Divide and simplify: $\frac{{3i}}{{5 + 2i}}$

Accepted Answer

$\frac{{6 + 15i}}{{29}}$

Answer

$\frac{{6 + 15i}}{{21}}$

Answer

$\frac{{6 - 15i}}{{21}}$

Answer

$\frac{{ - 6 - 15i}}{{29}}$

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