Complex Numbers Review

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

• No

Multiple Choice

Is the following in standard form?

 $21i+4$  

• Yes

• No

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.

 $25x^2+16$  

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

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

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

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