Calculate the modulus (R) and argument (θ) for z = 4 + 9i Give the argument between -π < θ < π.

R = 9.05, θ = 1.99 rad or 114°

R = 9.8, θ = 5.13 rad or 294°

Calculate the modulus (R) and argument (θ) for z = -5 + 3i Give the argument between -π < θ < π.

R = 5.83, θ = 2.6 rad or 149°

R = 5.83, θ = 0.54 rad or 31°

R = 5.83, θ = 3.7 rad or 211°

Calculate the modulus (R) and argument (θ) for z = -7 - 5i Give the argument between -π < θ < π.

R = 8.6, θ = -2.5 rad or -144.5°

R = 8.6, θ = 3.8 rad or 215.5°

R = 8.6 , θ = 4.1 rad or 234.5 °

Calculate the modulus (R) and argument (θ) for z = 3 - 7i Give the argument between -π < θ < π.

R = √58, θ = -1.2 rad or -66.8°

R = √58, θ = 5.1 rad or 293.2°

R = 7.6 , θ = 1.98 rad or 113.2 °

What is the shortcut rule for dividing complex numbers? z 1 z 2 \frac{z_1}{z_2} z 2 z 1

Divide their moduli and subtract their arguments ∣ z 1 ∣ ∣ z 2 ∣ a n d ( θ 1 − θ 2 ) \frac{\left|z_1\right|}{\left|z_2\right|}\ and\ \left(\theta_1-\theta_2\right) ∣ z 2 ∣ ∣ z 1 ∣ a n d ( θ 1 − θ 2 )

Add their moduli and multiply their arguments ∣ z 1 ∣ + ∣ z 2 ∣ a n d ( θ 1 × θ 2 ) \left|z_1\right|+\left|z_2\right|\ and\ \left(\theta_1\times\theta_2\right) ∣ z 1 ∣ + ∣ z 2 ∣ a n d ( θ 1 × θ 2 )

Multiply their moduli and add their arguments ∣ z 1 ∣ × ∣ z 2 ∣ a n d ( θ 1 + θ 2 ) \left|z_1\right|\times\left|z_2\right|\ and\ \left(\theta_1+\theta_2\right) ∣ z 1 ∣ × ∣ z 2 ∣ a n d ( θ 1 + θ 2 )

Subtract their moduli and divide their arguments ∣ θ 1 ∣ ∣ θ 2 ∣ a n d ( z 1 − z 2 ) \frac{\left|\theta_1\right|}{\left|\theta_2\right|}\ and\ \left(z_1-z_2\right) ∣ θ 2 ∣ ∣ θ 1 ∣ a n d ( z 1 − z 2 )

What is the shortcut rule for multiplying complex numbers? z 1 × z 2 z_1\times z_2 z 1 × z 2

Multiply their moduli and add their arguments ∣ z 1 ∣ × ∣ z 2 ∣ a n d ( θ 1 + θ 2 ) \left|z_1\right|\times\left|z_2\right|\ and\ \left(\theta_1+\theta_2\right) ∣ z 1 ∣ × ∣ z 2 ∣ a n d ( θ 1 + θ 2 )

Add their moduli and multiply their arguments ∣ z 1 ∣ + ∣ z 2 ∣ a n d ( θ 1 × θ 2 ) \left|z_1\right|+\left|z_2\right|\ and\ \left(\theta_1\times\theta_2\right) ∣ z 1 ∣ + ∣ z 2 ∣ a n d ( θ 1 × θ 2 )

Subtract their moduli and divide their arguments ∣ θ 1 ∣ ∣ θ 2 ∣ a n d ( z 1 − z 2 ) \frac{\left|\theta_1\right|}{\left|\theta_2\right|}\ and\ \left(z_1-z_2\right) ∣ θ 2 ∣ ∣ θ 1 ∣ a n d ( z 1 − z 2 )

Divide their moduli and subtract their arguments ∣ z 1 ∣ ∣ z 2 ∣ a n d ( θ 1 − θ 2 ) \frac{\left|z_1\right|}{\left|z_2\right|}\ and\ \left(\theta_1-\theta_2\right) ∣ z 2 ∣ ∣ z 1 ∣ a n d ( θ 1 − θ 2 )

Consider the complex number in the graph. Given that the argument must be between -π < θ < π, what can you say about the argument, θ?

θ is negative and -π < θ < -π/2

θ is negative and -π/2 < θ < 0

θ is positive and π/2 < θ < π

θ is positive and 0 < θ < π/2

Consider the complex number in the graph. Given that the argument must be between -π < θ < π, what can you say about the argument, θ?

θ is negative and -π/2 < θ < 0

θ is negative and -π < θ < -π/2

θ is positive and π/2 < θ < π

θ is positive and 0 < θ < π/2

Consider the complex number in the graph. Given that the argument must be between -π < θ < π, what can you say about the argument, θ?

θ is positive and π/2 < θ < π

θ is negative and -π < θ < -π/2

θ is negative and -π/2 < θ < 0

θ is positive and 0 < θ < π/2

Complex Numbers- Cartesian & find Modulus Argument

Authored by Kathryn Mendenhall

Mathematics

10th - 12th Grade

CCSS covered

Used 13+ times

Complex Numbers- Cartesian & find Modulus Argument

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19 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

In the complex plane, the horizontal axis if referred to as the axis and the vertical axis is called the _ axis

real, imaginary

imaginary, real

complex, standard

standard, cartesian

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Where is point C located?

2 + i

-3

-1 - i

Tags

CCSS.HSN.CN.B.4

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the right Argand's Diagram for z = 4 - 8i

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What complex number is shown on the graph?

(-2,-3)

-2-3i

2-3i

3i-2

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.B.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Match the expression to the graph shown in the complex plane.

(4,0)

4 + 4i

-4(i²)

Tags

CCSS.HSN.CN.B.4

CCSS.HSN.CN.A.1

CCSS.HSN.CN.B.5

CCSS.HSN.CN.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Simplify:
(2 - 3i)(5 + 4i)

22 - 7i

22 + 7i

22 - 7i²

22 + 7i²

Tags

CCSS.HSN.CN.C.8

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the complex conjugate of 4-3i?

A. 1/(4-3i)

B. 1/(4+3i)

C. -4 + 3i

D. 4 + 3i

Answer explanation

A conjugate of a complex number will have the same terms and an opposite +/- between them:

x = a + bi and it's conjugate is x = a - bi

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

One solution to the equation $x^2+px+q=0$ is x = 1 + 4i. What would the factored form (x - m)(x - n)=0 of the quadratic be?

$(X-(1+4i))(X-(1-4i))\ =0$

$(X+(1+4i))(X+(1-4i))=0$

$(X-(1+4i))(X-(1+4i))=0$

$(X-(1-4i))(X-(1-4i))=0$

Answer explanation

Factored form is (x - m)(x - n) = 0, where m and n are solutions (aka x-values) that make the equation equal zero.
If one solution is x = 1 +4i, then you plug that in for m.
The other solution will be the conjugate x = 1 -4i and you plug that in for n.
$(X-(1-4i))(X-(1-4i))=0$

Tags

CCSS.HSA.APR.B.3

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

One solution to the equation $x^2+px+q=0$ is x = 1 + 4i. You determine the factored form to be
$(X-(1+4i))(X-(1-4i))\ =0$
Use this to determine the standard form.

$x^2-2x+1-16i^2=0$

$x^2-2x+17=0$

$x^2+2x+1+8xi+4i-16i^2=0$

Answer explanation

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Complex Numbers- Cartesian & find Modulus Argument

In the complex plane, the horizontal axis if referred to as the axis and the vertical axis is called the _ axis

Where is point C located?

Find the right Argand's Diagram for z = 4 - 8i

What complex number is shown on the graph?

Match the expression to the graph shown in the complex plane.

Simplify:
(2 - 3i)(5 + 4i)

What is the complex conjugate of 4-3i?

A conjugate of a complex number will have the same terms and an opposite +/- between them:

x = a + bi and it's conjugate is x = a - bi

Let's say you're solving a quadratic using the quadratic formula, and determine that one solution is x = 3 + 2i. What is the other solution?

Every quadratic with complex solutions will have solutions in conjugate pairs:
x = a + bi and x = a - bi

If one solution is x = 3 + 2i, then the other solution will be x = 3 - 2i

One solution to the equation $x^2+px+q=0$ is x = 1 + 4i. What would the factored form (x - m)(x - n)=0 of the quadratic be?

Factored form is (x - m)(x - n) = 0, where m and n are solutions (aka x-values) that make the equation equal zero.
If one solution is x = 1 +4i, then you plug that in for m.
The other solution will be the conjugate x = 1 -4i and you plug that in for n.
$(X-(1-4i))(X-(1-4i))=0$

One solution to the equation $x^2+px+q=0$ is x = 1 + 4i. You determine the factored form to be
$(X-(1+4i))(X-(1-4i))\ =0$
Use this to determine the standard form.

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Complex Numbers- Cartesian & find Modulus Argument

In the complex plane, the horizontal axis if referred to as the ____ axis and the vertical axis is called the _____ axis

Where is point C located?

Find the right Argand's Diagram for z = 4 - 8i

What complex number is shown on the graph?

Match the expression to the graph shown in the complex plane.

Simplify:(2 - 3i)(5 + 4i)

What is the complex conjugate of 4-3i?

A conjugate of a complex number will have the same terms and an opposite +/- between them:x = a + bi and it's conjugate is x = a - bi

Let's say you're solving a quadratic using the quadratic formula, and determine that one solution is x = 3 + 2i. What is the other solution?

Every quadratic with complex solutions will have solutions in conjugate pairs:x = a + bi and x = a - biIf one solution is x = 3 + 2i, then the other solution will be x = 3 - 2i

One solution to the equation x2+px+q=0x^2+px+q=0x2+px+q=0 is x = 1 + 4i. What would the factored form (x - m)(x - n)=0 of the quadratic be?

One solution to the equation x2+px+q=0x^2+px+q=0x2+px+q=0 is x = 1 + 4i. You determine the factored form to be (X−(1+4i))(X−(1−4i)) =0(X-(1+4i))(X-(1-4i))\ =0(X−(1+4i))(X−(1−4i)) =0 Use this to determine the standard form.

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

In the complex plane, the horizontal axis if referred to as the axis and the vertical axis is called the _ axis

Simplify:
(2 - 3i)(5 + 4i)

A conjugate of a complex number will have the same terms and an opposite +/- between them:

x = a + bi and it's conjugate is x = a - bi

Every quadratic with complex solutions will have solutions in conjugate pairs:
x = a + bi and x = a - bi

If one solution is x = 3 + 2i, then the other solution will be x = 3 - 2i

One solution to the equation $x^2+px+q=0$ is x = 1 + 4i. What would the factored form (x - m)(x - n)=0 of the quadratic be?

One solution to the equation $x^2+px+q=0$ is x = 1 + 4i. You determine the factored form to be
$(X-(1+4i))(X-(1-4i))\ =0$
Use this to determine the standard form.