Question

A complex point of the form a 3i has a distance of 29 units from –9 24i. what is the value of a? –1 5 11 19.8

Answer 1

The value of a = 11

What is complex numbers ?

• Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”.
• The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = $\sqrt{( a - c)^{2} + (b -d )^{2} }$

put values in the formula -

$\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }$ = 29

square both sides

${(a + 9)^{2} + (21)^{2} } = 29^{2}$

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

Learn more about complex number

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