Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply and simplify the following complex numbers:

(1+5i)*(-3-i)

Multiply and simplify the following complex numbers: $\newline$ $(1+5 i) \cdot(-3-i)$

View step-by-step help

View step-by-step help

Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

(1+5 i) \cdot(-3-i)

Distribute terms: Distribute each term of the first complex number by each term of the second complex number. $\newline$ $(1+5i)(-3-i) = 1(-3) + 1(-i) + 5i(-3) + 5i(-i)$
Multiply terms: Multiply the terms. $\newline$ $1 \cdot (-3) = -3$ $\newline$ $1 \cdot (-i) = -i$ $\newline$ $5i \cdot (-3) = -15i$ $\newline$ $5i \cdot (-i) = 5i^2$ $\newline$ Since $i^2 = -1$ , we replace $5i^2$ with $5 \cdot (-1)$ .
Replace $i^2$ : Combine like terms and simplify. $\newline$ $-3 - i - 15i + 5*(-1)$ $\newline$ Combine the real parts: $-3 + 5*(-1) = -3 - 5 = -8$ $\newline$ Combine the imaginary parts: $-i - 15i = -16i$ $\newline$ So, the simplified form is $-8 - 16i$ .

More problems from Multiply numbers written in scientific notation

Question

16 a+72

to identify the equivalent expressions.

\newline

2

\newline

4(4 a+18)

\newline

8(2 a+9)

\newline

2(8+36 a)

\newline

2(8 a+72)

Posted 4 months ago

Question

30-6 v-18 w

to identify the equivalent expressions.

\newline

2

\newline

2(15-12 v)

\newline

3(10-3 v+6 w)

\newline

6(5-v-3 w)

\newline

2(15-3 v-9 w)

Posted 4 months ago

Question

24 m-12 p+72

to identify the equivalent expressions.

\newline

2

\newline

6(4 m+2 p+12)

\newline

2(12 m-6 p+36)

\newline

12(2 m-p+6)

\newline

24(m-12 p+3)

Posted 4 months ago

Question

48-8 x

to identify the equivalent expressions.

\newline

2

\newline

3(16-8 x)

\newline

2(24-4 x)

\newline

8(6-x)

\newline

4(12-4 x)

Posted 1 month ago

Question

Multiply and simplify the following complex numbers:

\newline

(-3-2 i) \cdot(-4+2 i)

Posted 3 months ago

Question

Multiply and simplify the following complex numbers:

\newline

(1-2 i) \cdot(4+i)

Posted 3 months ago

Question

Multiply and simplify the following complex numbers:

\newline

(-1+4 i) \cdot(4-3 i)

Posted 3 months ago

Question

Multiply and simplify the following complex numbers:

\newline

(-4-4 i) \cdot(-5-3 i)

Posted 3 months ago

Question

Multiply and simplify the following complex numbers:

\newline

(-2+2 i) \cdot(5+5 i)

Posted 3 months ago

Question

\newline

\newline

1

. a. Why does the bulb in the circuit given alongside in the figure not glow? Draw the circuit with the required change.

\newline

b. A coil suspended freely, points in North-South direction when no current is passed through it. Can you tell what will happen when a current is passed through it?

\newline

2

. Study the rainfall map of India as shown in figure.

16

4

. It gives the average annual rainfall in different regions of our country. Now, answer the following questions:

\newline

a. Locate on the map, the place you live in and write its name.

\newline

b. What is the annual rainfall in your region?

\newline

c. Is there a river or a lake ncar your cily/

1

own? Write Yes or No.

\newline

d. If yes, name the river or lake you have near your city/town.

\newline

e. Is there sufficient water available in your area throughout the year? Write Yes or No.

\newline

f. Itas your region suffered a drought in the past five years? Write Yes orNo.

\newline

g. Has your region suffered a flood in the past five years? Write Yes orNo.

Posted 9 hours ago