Practice Problems and Examples for Complex Numbers

Find the quotient $\frac{z_{1}}{z_{2}}$ of the complex numbers
$z_{1} = 50 (\cos \frac{4 π}{3} + i \sin \frac{4 π}{3})$ and
$z_{2} = 5 (\cos \frac{π}{3} + i \sin \frac{π}{3})$
Leave the answer in polar form.

Russell Gillen 2021-12-11

Add the following two complex numbers: $(3 + 2 i) + (5 - 3 i)$ . What do you notice?

Agohofidov6 2021-12-11

Prove that $e^{- i x} = \cos (x) - i \sin (x)$

Walter Clyburn 2021-12-10

Find the real numbers x and y that make the equation true.
$2 + 3 i = x + y i$

3kofbe 2021-11-14

To find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2. Find a rational number halfway between the two fractions in each pair. 1/100 and 1/10

madeleinejames20 2021-06-08

part of $10,000 is invested at 11% simple interest account, the rest is at 14% simple interest account. If the annual income is $1,265, how much is invested at each rate?

necessaryh 2021-03-11

Determine the absolute value of each of the following complex numbers:
a. $z = 5 + 12 i$
b. $2 - 3 i .$

ringearV 2021-02-26

Find the product of the complex numbers.Leave answers in polar form.
$z_{1} = 1 + i$
$z_{2} = - 1 + i$

defazajx 2021-02-15

Write the complex number in trigonometric form $r (\cos θ + i \sin θ)$ ,with theta in the interval $[0^{\circ}, 360^{\circ}]$
$5 \sqrt{3} + 5 i$

Yulia 2021-02-14

Find the modulus of each of the complex numbers 5i, 7, and 3 + 4i.

Chesley 2021-02-12

Find the real numbers x and y so that the equation is true. $x - 2 i = 7 + y i$

Line 2021-02-09

How to add complex numbers. Provide an example with your explanation.

shadsiei 2021-02-02

The exponential expression $2^{8}$ has a value of 256. Write two other exponential expressions that have a value of 256. Explain how you got your answers. (Begin by writing out $2^{8}$ as the product of 2s.)

floymdiT 2021-02-01

$(- 5) \times \dots \times (- 5) 17 t i m e s$

Isa Trevino 2021-01-31

If z is a complex number, show that the sum of z and its conjugate is a real number.

Kye 2021-01-24

Write each complex number in standard form. $2 (\cos 30^{\circ} + i \sin 30^{\circ})$

Tazmin Horton 2021-01-17

In the example problem, $2.4 x 10^{6}$ was rewritten as $24 x 10^{5}$ . Explain why those expressions are equivalent.

CoormaBak9 2021-01-07

Write standart form of complex number $5 ({\cos 135}^{\circ} + i {\sin 135}^{\circ})$

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Precalculus