Add the following together. ( − 4 − 3 i ) + ( − 3 + 2 i ) \left(-4-3i\right)+\left(-3+2i\right) ( − 4 − 3 i ) + ( − 3 + 2 i )

− 1 − 5 i -1-5i − 1 − 5 i

Subtract the following. ( 4 + 7 i ) − ( 1 + i ) \left(4+7i\right)-\left(1+i\right) ( 4 + 7 i ) − ( 1 + i )

− 3 + 11 i -3+11i − 3 + 1 1 i

Multiply the following together. ( − 3 − 3 i ) ( − 2 − i ) \left(-3-3i\right)\left(-2-i\right) ( − 3 − 3 i ) ( − 2 − i )

− 5 − 4 i -5-4i − 5 − 4 i

Simplify 4 + 3 i 2 i \frac{4+3i}{2i} 2 i 4 + 3 i

3 2 − 2 i \frac{3}{2}-2i 2 3 − 2 i

− 2 + 3 2 i -2+\frac{3}{2}i − 2 + 2 3 i

− 5 − 2 i -5-2i − 5 − 2 i

Simplify 3 − 2 i 10 i \frac{3-2i}{10i} 1 0 i 3 − 2 i

− 1 5 − 3 10 i -\frac{1}{5}-\frac{3}{10}i − 5 1 − 1 0 3 i

1 5 + 3 10 i \frac{1}{5}+\frac{3}{10}i 5 1 + 1 0 3 i

− 5 − 3 i -5-3i − 5 − 3 i

Simplify 1 + i 2 − 3 i \frac{1+i}{2-3i} 2 − 3 i 1 + i

− 1 13 + 5 13 i -\frac{1}{13}+\frac{5}{13}i − 1 3 1 + 1 3 5 i

1 13 − 5 13 i \frac{1}{13}-\frac{5}{13}i 1 3 1 − 1 3 5 i

Simplify 4 − 5 i 2 + 4 i \frac{4-5i}{2+4i} 2 + 4 i 4 − 5 i

− 3 5 − 13 10 i -\frac{3}{5}-\frac{13}{10}i − 5 3 − 1 0 1 3 i

− 3 − 13 i -3-13i − 3 − 1 3 i

− 5 − 10 i -5-10i − 5 − 1 0 i

3 5 + 13 10 i \frac{3}{5}+\frac{13}{10}i 5 3 + 1 0 1 3 i

Find the modulus of the complex number. z = 2 + 5 i z=2+5i z = 2 + 5 i

∣ z ∣ = 29 \left|z\right|=\sqrt{29} ∣ z ∣ = 2 9 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 5 \left|z\right|=5 ∣ z ∣ = 5

∣ z ∣ = 2 7 \left|z\right|=2\sqrt{7} ∣ z ∣ = 2 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 7 2 \left|z\right|=7\sqrt{2} ∣ z ∣ = 7 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Find the modulus of the complex number. z = − 4 − 7 i z=-4-7i z = − 4 − 7 i

∣ z ∣ = 65 \left|z\right|=\sqrt{65} ∣ z ∣ = 6 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 56 \left|z\right|=\sqrt{56} ∣ z ∣ = 5 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 65 \left|z\right|=65 ∣ z ∣ = 6 5

∣ z ∣ = 56 \left|z\right|=56 ∣ z ∣ = 5 6

Find the modulus of the complex number. z = 3 + i z=3+i z = 3 + i

∣ z ∣ = 10 \left|z\right|=\sqrt{10} ∣ z ∣ = 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 10 \left|z\right|=10 ∣ z ∣ = 1 0

∣ z ∣ = 2 \left|z\right|=2 ∣ z ∣ = 2

∣ z ∣ = 2 \left|z\right|=\sqrt{2} ∣ z ∣ = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Complex Numbers Review

Presentation

•

Mathematics

•

10th Grade

•

Practice Problem

•

Medium

•

CCSS

HSN.CN.A.2, HSN.CN.A.3, HSA.APR.C.4

Standards-aligned

Used 24+ times

FREE Resource

8 Slides • 25 Questions

Complex Numbers Review

G11 Quiz Review

Standard Form

Complex Numbers need to be in Standard Form
Real Numbers first then Imaginary Numbers
a + bi

Complex Numbers

Made of Real and Imaginary Numbers
What is the difference between real and imaginary?

Multiple Choice

Is the following in standard form?

-6-7i

Yes

Multiple Choice

Is the following in standard form?

21i+4

Yes

Operations with Complex Numbers

Adding and Subtracting
Multiplying
Dividing (CONJUGATE)

Multiple Choice

Add the following together.

\left(3+5i\right)+\left(7+i\right)

$4+4i$

$10+6i$

$21+5i$

$10+5i$

Multiple Choice

Add the following together.

\left(-4-3i\right)+\left(-3+2i\right)

$-7-i$

$-1-i$

$12-6i$

$-1-5i$

Multiple Choice

Subtract the following.

\left(4+7i\right)-\left(1+i\right)

$5+8i$

$-3+11i$

$3+6i$

$3+7i$

Multiple Choice

Subtract the following.

\left(-3-6i\right)-\left(4-5i\right)

$-7-i$

$7+i$

$1-i$

$12+30i$

Multiple Choice

Multiply the following together.

\left(2+i\right)\left(3+2i\right)

$8+7i$

$12+12i$

$4+7i$

$4+i$

Multiple Choice

Multiply the following together.

\left(2+3i\right)\left(4-6i\right)

$26$

$26i$

$26+24i$

$62$

Multiple Choice

Multiply the following together.

\left(-3-3i\right)\left(-2-i\right)

$-5-4i$

$9+9i$

$3+3i$

$3+9i$

Multiple Choice

Multiply the following together.

\left(4+2i\right)\left(4-2i\right)

$20$

$20i$

$20+16i$

$16+20i$

Multiple Choice

Simplify

\left(7+i\right)^2

$14+48i$

$48+14i$

$14+i^2$

$13$

Division (CONJUGATE)

No i in the denominator
Multiply the conjugate
a + bi its conjugate is a - bi

Multiple Choice

Simplify

\frac{4+3i}{2i}

$\frac{3}{2}-2i$

$-2+\frac{3}{2}i$

$-5-2i$

$2+0i$

Multiple Choice

Simplify

\frac{3-2i}{10i}

$-\frac{1}{5}-\frac{3}{10}i$

$\frac{1}{5}+\frac{3}{10}i$

$-5-3i$

$5+3i$

Multiple Choice

Simplify

\frac{1+i}{2-3i}

$\frac{1}{13}-\frac{5}{13}i$

$-\frac{1}{13}+\frac{5}{13}i$

$-1+5i$

$1-5i$

Multiple Choice

Simplify

\frac{4-5i}{2+4i}

$-3-13i$

$-5-10i$

$-\frac{3}{5}-\frac{13}{10}i$

$\frac{3}{5}+\frac{13}{10}i$

Modulus of Complex Numbers

$z=a+bi$
$\left|z\right|=\sqrt{a^2+b^2}$

Multiple Choice

Find the modulus of the complex number.

z=2+5i

$\left|z\right|=\sqrt{29}$

$\left|z\right|=5$

$\left|z\right|=2\sqrt{7}$

$\left|z\right|=7\sqrt{2}$

Multiple Choice

Find the modulus of the complex number.

z=-4-7i

$\left|z\right|=\sqrt{56}$

$\left|z\right|=65$

$\left|z\right|=\sqrt{65}$

$\left|z\right|=56$

Multiple Choice

Find the modulus of the complex number.

z=3+i

$\left|z\right|=10$

$\left|z\right|=\sqrt{10}$

$\left|z\right|=2$

$\left|z\right|=\sqrt{2}$

Quadratics with Complex Solutions

$i^2=-1$

Multiple Choice

Solve the following equation.

x^2=-4

$x=2i$

$x=i\sqrt{4}$

$x=2i\sqrt{2}$

$No\ Solution$

Multiple Choice

Solve the following equation.

\left(x+1\right)^2=-1

$x=1-i$

$x=-1+i$

$x=3$

$x=1+2i$

Multiple Choice

Solve the following equation.

\left(3x+2\right)^2=-18

$x=-\frac{2}{3}+i\sqrt{2}$

$x=-2+3i\sqrt{2}$

$x=-\frac{2}{3}+3i\sqrt{2}$

$x=-\frac{3}{2}+i\sqrt{2}$

Writing Polynomials as Complex Numbers

$a^2+b^2$
$\left(a+bi\right)\left(a-bi\right)$

Multiple Choice

Factor the following.

x^2+9

$\left(x+3i\right)\left(x-3i\right)$

$\left(x-3i\right)\left(x-3i\right)$

$\left(x+3i\right)\left(x+3i\right)$

$\left(x+9i\right)\left(x-9i\right)$

Multiple Choice

Factor the following.

x^2+7

$\left(x+\sqrt{7i}\right)\left(x-\sqrt{7i}\right)$

$\left(x+i\sqrt{7}\right)\left(x-i\sqrt{7}\right)$

$\left(x+i\sqrt{7}\right)\left(x+i\sqrt{7}\right)$

$\left(x+7i\right)\left(x-7i\right)$

Multiple Choice

Factor the following.

25x^2+16

$\left(5x+4i\right)\left(5x-4i\right)$

$\left(4x+5i\right)\left(4x-5i\right)$

$\left(5x+4\right)\left(5x+4\right)$

$\left(5x+4\right)\left(5x-4\right)$

Multiple Choice

Factor the following.

25x^2+16

$\left(5x+4i\right)\left(5x-4i\right)$

$\left(4x+5i\right)\left(4x-5i\right)$

$\left(5x+4\right)\left(5x+4\right)$

$\left(5x+4\right)\left(5x-4\right)$

Complex Numbers Review

G11 Quiz Review

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