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ANTONII [103]
3 years ago
14

Please can someone help me ?

Mathematics
2 answers:
anygoal [31]3 years ago
5 0

Answer:

-3-5i

Step-by-step explanation:


Eddi Din [679]3 years ago
4 0

z = -14 + 21i / -2 - 4i


Rectangular form:

z = -14-14.5i


Exponential form:

z = 20.155644 × ei (-133°59'42″)


Polar form:

z = 20.155644 × (cos (-133°59'42″) + i sin (-133°59'42″))


Polar form - absolute value (modulus) and angle (argument):

r = |z| = 20.15564

φ = arg z = -133.99491° = -133°59'42″ = -0.74442π


Calculation steps


   Divide: 21i / (-2) = -10.5i

   Add: -14 + (-10.5i) = -14-10.5i

   Subtract: (-14-10.5i) - 4i = -14 + (-10.5-4)i = -14-14.5i




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As it has been given that x=4+5i, y=2-9i.

We need to find the value of the following:

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(ii) -x+3y, substituting the value of 'x' and 'y' in the expression, we get:

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(iii) x \times y, we need to substitute the value of 'x' and 'y' in the expression,  for this, we can use distributive property of multiplication that says,

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Using the distributive property of multiplication:

(4+5i)\times(2-9i)=4 \times 2-4 \times 9i+5i \times 2-5i \times 9i

=8-36i+10i-45i^2

Now, we know that i \times i=i^2=-1

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Therefore, x \times y=53-26i.

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2(4+5i)\times (2-9i)

Again, we can use distributive property of multiplication that says,

a(b+c)=a \times b+ a \times c

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2(4+5i) \times (2-9i)=2\times 4+2 \times 5i\times(2-9i)

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since, i^2=-1

we get,

16-72i+20i-90 \times (-1)=16-52i+90

=106-52i

Therefore,

2x \times y=106-52i


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