Simplify (-3i)(7i)(-1)
Last Updated :
22 Dec, 2023
Complex number is the sum of a real number and an imaginary number. These are the numbers that can be written in the form of a+ib, where a and b both are real numbers. It is denoted by z.
For example:
- 3+4i is a complex number, where 3 is a real number (Re) and 4i is an imaginary number (Im).
- 2+5i is a complex number where 2 is a real number (Re) and 5i is an imaginary number (im)
The combination of real number and imaginary number is called a Complex number
Example: √-3, √-7, √-11 are all imaginary numbers. here ‘i’ is an imaginary number called “iota”.
Rules of Imaginary Numbers
i = √-1
i2 = -1
i3 = -i
i4 = 1
i4n = 1
i4n-1 = -1
Simplify (-3i)(7i)(-1)
Solution:
Given: (-3i)(7i)(-1)
= -3i x 7i x (-1)
= -21i2 x -1 {i2 = -1}
= -21 (-1) x -1
= 21 x -1
= -21 + 0i
Similar Questions
Question 1: Express the problem in a+ib, (-5i)(1/8i)
Solution:
Given: (-5i)(1/8i)
= -5/8 i2
= -5/8 (-1) {i2 = -1}
= 5/8 + 0i
Question 2: Express the problem in a+ib, i9 + i19?
Solution:
Given: i9 + i19
= (i 4 )2i + (i4 )4 i3
= (1)2 i + (1)4 i3 {i4 = 1}
= i + i3
= i + (-i) {i3 = -i}
= i – i
= 0 + 0i
Question 3: Express in form of a+ib, {3(7+7i) + i(7+7i)}?
Solution:
Given : {3(7+7i) + i(7+7i)}
= {21 +21i + 7i + 7i2}
= {21 + 28i + 7(-1)}
= {21 + 28i – 7}
= 14 + 28i
= 14 + 28i
Question 4: Express in form of a + bi, 1/(3-4i)?
Solution:
Given : 1/(3-4i)
= 1/(3-4i) x (3+4i)/(3+4i)
= (3+4i) / {(3)2 – (4i)2}
= (3+4i) / {9 + 16}
= (3+4i) / 25
= 3/25 + (4/25)i
Question 5: Simplify (3 + 4i) / (3 + 2i)
Solution:
Multiplying the numerator and denominator with the conjugate of denominators.
= ((3 + 4i) * (3 – 2i)) / ((3 + 2i) * (3 – 2i))
= (9 -6i +12i – 8i2 ) / {9 -(2i)2 }
= (17 + 6i) / (13)
= (17+ 6i) / 13
Question 6: Simplify (4 + 4i)*(3 – 4i)
Solution:
Given : (4 + 4i)*(3 – 4i)
= (12+ 12i -16i – 16i2 )
= 12 -4i +16
= 28 – 4i
Question 7: Simplify {(-3 – 5i) / (2 +2i)}?
Solution:
Given {(-3 – 5i) / (2 +2i) }
conjugate of denominator 2+2i is 2-2i
Multiply the numerator and denominator with the conjugate
Therefore {(-3 – 5i) / (2 +2i) } x {(2-2i) / (2-2i) }
= {-6 -6i -10i +10i2 } / { 22 – (2i)2 } {difference of squares formula . i.e (a+b)(a-b) = a2 – b2 }
= {-6 -6i -10i + 10 (-1) } / { 4 – 4(-1) } { i2 = -1 }
= {-6 -6i -10i -10 } / { 4 + 4 }
= (-16 – 16i ) / 8
= -16 /8 – 16i /8
= -2 -2i
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