# Write the complex number z in two algebraic form. z = sqrt2*(cos pi/2 + i sin pi/2)

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giorgiana1976 | Student

The given complex number z is given under the trigonometric form:

z = |z|*(cos t+ i*sin t)

where:

|z| = sqrt (a^2 + b^2)

cos t = a / |z| and sint = b / |z|

We'll identify a,b,|z|:

|z| = sqrt2

cos pi/2 = a/|z|

0 = a/sqrt2

a = 0*sqrt2

**a = 0**

sin pi/2 = b / |z|

1 = b / sqrt2

**b =sqrt2**

Now, we'll put z under the algebraic form:

z = a+b*i, where a is the real part and b is the imaginary part.

z = 0 + i*sqrt2

**z = i*sqrt2**

neela | Student

The given complex number Z = sqrt2*(cospi/2 +i sinpi/2)

We know that cospi/2 = 0 and sin pi/2 = 1.

So the given complex number z = sqrt2 {cospi/2 +isinpi/2) = (sqrt2)(0+i) = (sqrt2)i

Also sqrt2(cospi+isinp/2) = e^(i*pi/2) is another form of writing in the exponent form which is due to Euler.