Evaluate the expression and write your answer in the form a + bi. 1) (2-6i)+(4+2i)2) (6+5i)(9-2i)3) 2/(3-9i)4) (3 − 5i)(7 − 2i)

  Simplified form of the given expressions will be,

1). 6 - 4i

2). 64 + 33i

3).

4).

1). In a complex number (a + bi),

    a = Real part of the complex number

   bi = Imaginary part

     Expression given in the question → (2 - 6i) + (4 + 2i)

Rule to solve the given expression,

"Add real part and imaginary part of two complex numbers separately"

(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)

                         = 6 + (-4i)

                         = 6 - 4i

  Therefore, simplified form of the given expression will be (6 - 4i).

2). Given expression → (6 + 5i)(9 - 2i)

Rule to solve the expression → i² = -1

(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)

                       = 54 - 12i + 45i - 10i²

                       = 54 - 12i + 45i + 10 [Since, i² = -1]

                       = (54 + 10) + (45i - 12i)

                       = 64 + 33i

     Therefore, simplified form of the given expression will be (64 + 33i).

3). Given expression →

Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).

    Therefore, simplified form of the given expression will be

4). Given expression →

Multiply numerator and denominator with the conjugate of the denominator.

  Therefore, simplified form of the given expression will be .

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Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

gmt is 4 hrs ahead of edt so just add four hours to 1: 14: 20 (minutes and seconds stay the same)

gmt is 5: 14: 20

hope this !

~just a girl in love with shawn mendes